Experimental Probability
Experimental probability: introduction, experimental probability: definition, experimental probability formula, solved examples, practice problems, frequently asked questions.
In mathematics, probability refers to the chance of occurrence of a specific event. Probability can be measured on a scale from 0 to 1. The probability is 0 for an impossible event. The probability is 1 if the occurrence of the event is certain.
There are two approaches to study probability: experimental and theoretical.
Suppose you and your friend toss a coin to decide who gets the first turn to ride a new bicycle. You choose “heads” and your friend chooses “tails.”
Can you guess who will win? No! You have $\frac{1}{2}$ a chance of winning and so does your friend. This is theoretical since you are predicting the outcome based on what is expected to happen and not on the basis of outcomes of an experiment.
So, what is the experimental probability? Experimental probability is calculated by repeating an experiment and observing the outcomes. Let’s understand this a little better.
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Experimental probability, or empirical probability, is the probability calculated by performing actual experiments and gathering or recording the necessary information. How would you define an experiment? The math definition of an experiment is “a process or procedure that can be repeated and that has a set of well-defined possible results or outcomes.”
Consider the same example. Suppose you flip the coin 50 times to see whether you get heads or tails, and you record the outcomes. Suppose you get heads 20 times and tails 30 times. Then the probability calculated using these outcomes is experimental probability. Here, t he experimental meaning is connected with such experiments used to determine the probability of an event.
Now that you know the meaning of experimental probability, let’s understand its formula.
Experimental Probability for an Event A can be calculated as follows:
P(E) $= \frac{Number of occurance of the event A}{Total number of trials}$
Let’s understand this with the help of the last example.
A coin is flipped a total of 50 times. Heads appeared 20 times. Now, what is the experimental probability of getting heads?
E xperimental probability of getting heads $= \frac{Number of occurrences}{Total number of trials}$
P (Heads) $= \frac{20}{50} = \frac{2}{5}$
P (Tails) $= \frac{30}{50} = \frac{3}{5}$
Experimental Probability vs. Theoretical Probability
Theoretical probability expresses what is expected. On the other hand, experimental probability explains how frequently an event occurred in an experiment.
If you roll a die, the theoretical probability of getting any particular number, say 3, is $\frac{1}{6}$.
However, if you roll the die 100 times and record how many times 3 appears on top, say 65 times, then the experimental probability of getting 3 is $\frac{65}{100}$.
Theoretical probability for Event A can be calculated as follows:
P(A) $= \frac{Number of outcomes favorable to Event A}{Number of possible outcomes}$
In the example of flipping a coin, the theoretical probability of the occurrence of heads (or tails) on tossing a coin is
P(H) $= \frac{1}{2}$ and P(T) $= \frac{1}{2}$ (since possible outcomes are $2 -$ head or tail)
Experimental Probability: Examples
Let’s take a look at some of the examples of experimental probability .
Example 1: Ben tried to toss a ping-pong ball in a cup using 10 trials, out of which he succeeded 4 times.
P(win) $= \frac{Number of success}{Number of trials}$
$= \frac{4}{10}$
$= \frac{2}{5}$
Example 2: Two students are playing a game of die. They want to know how many times they land on 2 on the dice if the die is rolled 20 times in a row.
The experimental probability of rolling a 2
$= \frac{Number of times 2 appeared}{Number of trials}$
$= \frac{5}{20}$
$= \frac{1}{4}$
1. Probability of an event always lies between 0 and 1.
2. You can also express the probability as a decimal and a percentage.
Experimental probability is a probability that is determined by the results of a series of experiments. Learn more such interesting concepts at SplashLearn .
1. Leo tosses a coin 25 times and observes that the “head” appears 10 times. What is the experimental probability of getting a head?
P(Head) $= \frac{Number of times heads appeared}{Total number of trials}$
$= \frac{10}{25}$
$= \frac{2}{5}$
$= 0.4$
2. The number of cakes a baker makes per day in a week is given as 7, 8, 6, 10, 2, 8, 3. What is the probability that the baker makes less than 6 cakes the next day?
Solution:
Number of cakes baked each day in a week $= 7, 8, 6, 10, 2, 8, 3$
Out of 7 days, there were 2 days (highlighted in bold) on which the baker made less than 6 cookies.
P$(< 6 $cookies$) = \frac{2}{7}$
3. The chart below shows the number of times a number was shown on the face of a tossed die. What was the probability of getting a 3 in this experiment?
Number of times 3 showed $= 7$
Number of tosses $= 30$
P(3) $= \frac{7}{30}$
4. John kicked a ball 20 times. He kicked 16 field goals and missed 4 times . What is the experimental probability that John will kick a field goal during the game?
Solution:
John succeeded in kicking 16 field goals. He attempted to kick a field goal 20 times.
So, the number of trials $= 20$
John’s experimental probability of kicking a field goal $= \frac{Successful outcomes} {Trials attempted} = \frac{16}{20}$
$= \frac{4}{5}$
$= 0.8$ or $80%$
5. James recorded the color of bikes crossing his street. Of the 500 bikes, 10 were custom colors, 100 were white, 50 were red, 120 were black, 100 were silver, 60 were blue, and 60 were gray. What is the probability that the car crossing his street is white?
Number of white bikes $= 100$
Total number of bikes $= 500$
P(white bike) $= \frac{100}{500} = \frac{1}{5}$
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In a class, a student is chosen randomly in five trials to participate in 5 different events. Out of chosen students, 3 were girls and 2 were boys. What is the experimental probability of choosing a boy in the next event?
A manufacturer makes 1000 tablets every month. after inspecting 100 tablets, the manufacturer found that 30 tablets were defective. what is the probability that you will buy a defective tablet, the 3 coins are tossed 1000 times simultaneously and we get three tails $= 160$, two tails $= 260$, one tail $= 320$, no tails $= 260$. what is the probability of occurrence of two tails, the table below shows the colors of shirts sold in a clothing store on a particular day and their respective frequencies. use the table to answer the questions that follow. what is the probability of selling a blue shirt.
Jason leaves for work at the same time each day. Over a period of 327 working days, on his way to work, he had to wait for a train at the railway crossing for 68 days. What is the experimental probability that Jason has to wait for a train on his way to work?
What is the importance of experimental probability?
Experimental probability is widely used in research and experiments in various fields, such as medicine, social sciences, investing, and weather forecasting.
Is experimental probability always accurate?
Predictions based on experimental probability are less reliable than those based on theoretical probability.
Can experimental probability change every time the experiment is performed?
Since the experimental probability is based on the actual results of an experiment, it can change when the results of an experiment change.
What is theoretical probability?
The theoretical probability is calculated by finding the ratio of the number of favorable outcomes to the total number of probable outcomes.
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Experimental Probability
The chance or occurrence of a particular event is termed its probability. The value of a probability lies between 0 and 1 which means if it is an impossible event, the probability is 0 and if it is a certain event, the probability is 1. The probability that is determined on the basis of the results of an experiment is known as experimental probability. This is also known as empirical probability.
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What is Experimental Probability?
Experimental probability is a probability that is determined on the basis of a series of experiments. A random experiment is done and is repeated many times to determine their likelihood and each repetition is known as a trial. The experiment is conducted to find the chance of an event to occur or not to occur. It can be tossing a coin, rolling a die, or rotating a spinner. In mathematical terms, the probability of an event is equal to the number of times an event occurred ÷ the total number of trials. For instance, you flip a coin 30 times and record whether you get a head or a tail. The experimental probability of obtaining a head is calculated as a fraction of the number of recorded heads and the total number of tosses. P(head) = Number of heads recorded ÷ 30 tosses.
Experimental Probability Formula
The experimental probability of an event is based on the number of times the event has occurred during the experiment and the total number of times the experiment was conducted. Each possible outcome is uncertain and the set of all the possible outcomes is called the sample space. The formula to calculate the experimental probability is: P(E) = Number of times an event occurs/Total number of times the experiment is conducted
Consider an experiment of rotating a spinner 50 times. The table given below shows the results of the experiment conducted. Let us find the experimental probability of spinning the color - blue.
| Color | Occurrences |
|---|---|
| Pink | 11 |
| Blue | 10 |
| Green | 13 |
| Yellow | 16 |
The experimental probability of spinning the color blue = 10/50 = 1/5 = 0.2 = 20%
Experimental Probability vs Theoretical Probability
Experimental results are unpredictable and may not necessarily match the theoretical results. The results of experimental probability are close to theoretical only if the number of trials is more in number. Let us see the difference between experimental probability and theoretical probability.
| It is based on the data which is obtained after an experiment is carried out. | This is based on what is expected to happen in an experiment, without actually conducting it. |
| It is the result of: the number of occurrences of an event ÷ the total number of trials | It is the result of: the number of favorable outcomes ÷ the total number of possible outcomes |
| Example: A coin is tossed 20 times. It is recorded that heads occurred 12 times and tails occurred 8 times. P(heads)= 12/20= 3/5 P(tails) = 8/20 = 2/5 | Example: A coin is tossed. P(heads) = 1/2 P(tails) =1/2 |
Experimental Probability Examples
Here are a few examples from real-life scenarios.
a) The number of cookies made by Patrick per day in this week is given as 4, 7, 6, 9, 5, 9, 5.
Based on this data, what is the reasonable estimate of the probability that Patrick makes less than 6 cookies the next day?
P(< 6 cookies) = 3/7 = 0.428 = 42%
b) Find the reasonable estimate of the probability that while ordering a pizza, the next order will not be of a pepperoni topping.
| Pizza Toppings | Number of orders |
|---|---|
| Mushrooms | 4 |
| Pepperoni | 5 |
| Cheese | 7 |
| Black Olives | 4 |
Based on this data , the reasonable estimate of the probability that the next type of toppings that would get ordered is not a pepperoni will be 15/20 = 3/4 = 75%
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Important Notes
- The sum of the experimental probabilities of all the outcomes is 1.
- The probability of an event lies between 0 and 1, where 0 is an impossible event and 1 denotes a certain event.
- Probability can also be expressed in percentage.
Examples on Experimental Probability
Example 1: The following table shows the recording of the outcomes on throwing a 6-sided die 100 times.
| 1 | 14 |
| 2 | 18 |
| 3 | 24 |
| 4 | 17 |
| 5 | 13 |
| 6 | 14 |
Find the experimental probability of: a) Rolling a four; b) Rolling a number less than four; c) Rolling a 2 or 5
Experimental probability is calculated by the formula: Number of times an event occurs/Total number of trials
a) Rolling a 4: 17/100 = 0.17
b) Rolling a number less than 4: 56/100 = 0.56
c) Rolling a 2 or 5: 31/100 = 0.31
Example 2: The following set of data shows the number of messages that Mike received recently from 6 of his friends. 4, 3, 2, 1, 6, 8. Based on this, find the probability that Mike will receive less than 2 messages next time.
Mike has received less than 2 messages from 2 of his friends out of 6.
Therefore, P(<2) = 2/6 = 1/3
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Practice Questions on Experimental Probability
Frequently asked questions (faqs), how do you find the experimental probability.
The experimental probability of an event is based on actual experiments and the recordings of the events. It is equal to the number of times an event occurred divided by the total number of trials.
What is the Experimental Probability of rolling a 6?
The experimental probability of rolling a 6 is 1/6. A die has 6 faces numbered from 1 to 6. Rolling the die to get any number from 1 to 6 is the same and the probability (of getting a 6) = Number of favorable outcomes/ total possible outcomes = 1/6.
What is the Difference Between Theoretical and Experimental Probability?
Theoretical probability is what is expected to happen and experimental probability is what has actually happened in the experiment.
Do You Simplify Experimental Probability?
Yes, after finding the ratio of the number of times the event occurred to the total number of trials conducted, the fraction which is obtained is simplified.
Which Probability is More Accurate, Theoretical Probability or Experimental Probability?
Theoretical probability is more accurate than experimental probability. The results of experimental probability are close to theoretical only if the number of trials are more in number.
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- Experimental Probability
You and your 3 friends are playing a board game. It’s your turn to roll the die and to win the game you need a 5 on the dice. Now, is it possible that upon rolling the die you will get an exact 5? No, it is a matter of chance. We face multiple situations in real life where we have to take a chance or risk. Based on certain conditions, the chance of occurrence of a certain event can be easily predicted. In our day to day life, we are more familiar with the word ‘ chance and probability ’. In simple words, the chance of occurrence of a particular event is what we study in probability. In this article, we are going to discuss one of the types of probability called “Experimental Probability” in detail.
What is Probability?
Probability, a branch of Math that deals with the likelihood of the occurrences of the given event. The probability values for the given experiment is usually defined between the range of numbers. The values lie between the numbers 0 and 1. The probability value cannot be a negative value. The basic rules such as addition, multiplication and complement rules are associated with the probability.
Experimental Probability Vs Theoretical Probability
There are two approaches to study probability:
- Theoretical Probability
What is Experimental Probability?
Experimental probability, also known as Empirical probability, is based on actual experiments and adequate recordings of the happening of events. To determine the occurrence of any event, a series of actual experiments are conducted. Experiments which do not have a fixed result are known as random experiments. The outcome of such experiments is uncertain. Random experiments are repeated multiple times to determine their likelihood. An experiment is repeated a fixed number of times and each repetition is known as a trial. Mathematically, the formula for the experimental probability is defined by;
Probability of an Event P(E) = Number of times an event occurs / Total number of trials.
What is Theoretical Probability?
In probability, the theoretical probability is used to find the probability of an event. Theoretical probability does not require any experiments to conduct. Instead of that, we should know about the situation to find the probability of an event occurring. Mathematically, the theoretical probability is described as the number of favourable outcomes divided by the number of possible outcomes.
Probability of Event P(E) = No. of. Favourable outcomes/ No. of. Possible outcomes.
Experimental Probability Example
Example: You asked your 3 friends Shakshi, Shreya and Ravi to toss a fair coin 15 times each in a row and the outcome of this experiment is given as below:
| Shakshi | 6 | 9 |
| Shreya | 7 | 8 |
| Ravi | 8 | 7 |
Calculate the probability of occurrence of heads and tails.
Solution: The experimental probability for the occurrence of heads and tails in this experiment can be calculated as:
Experimental Probability of Occurrence of heads = Number of times head occurs/Number of times coin is tossed.
Experimental Probability of Occurrence of tails = Number of times tails occurs/Number of times coin is tossed.
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| Shakshi | 6 | 9 | 6/15 = 0.4 | 9/15 = 0.6 |
| Shreya | 7 | 8 | 7/15 = 0.47 | 8/15 = 0.53 |
| Ravi | 8 | 7 | 8/15 = 0.53 | 7/15 = 0.47 |
We observe that if the number of tosses of the coin increases then the probability of occurrence of heads or tails also approaches to 0.5.
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What is experimental probability?
Practice questions, experimental probability – explanation & examples.
Experimental probability is the probability determined based on the results from performing the particular experiment.
In this lesson we will go through:
- The meaning of experimental probability
- How to find experimental probability
The ratio of the number of outcomes favorable to an event to the total number of trials of the experiment.
Experimental Probability can be expressed mathematically as:
$P(\text{E}) = \frac{\text{number of outcomes favorable to an event}}{\text{total number of trials of the experiment}}$
Let’s go back to the die tossing example. If after 12 throws you get one 6, then the experimental probability is $\frac{1}{12}$. You can compare that to the theoretical probability. The theoretical probability of getting a 6 is $\frac{1}{6}$. This means that in 12 throws we would have expected to get 6 twice.
Similarly, if in those 12 tosses you got a 1 five times, the experimental probability is $\frac{5}{12}$.
How do we find experimental probability?
Now that we understand what is meant by experimental probability, let’s go through how it is found.
To find the experimental probability of an event, divide the number of observed outcomes favorable to the event by the total number of trials of the experiment.
Let’s go through some examples.
Example 1: There are 20 students in a class. Each student simultaneously flipped one coin. 12 students got a Head. From this experiment, what was the experimental probability of getting a head?
Number of coins showing Heads: 12
Total number of coins flipped: 20
$P(\text{Head}) = \frac{12}{20} = \frac{3}{5}$
Example 2: The tally chart below shows the number of times a number was shown on the face of a tossed die.
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1 | 4 |
2 | 6 |
3 | 7 |
4 | 8 |
5 | 2 |
6 | 3 |
a. What was the probability of a 3 in this experiment?
b. What was the probability of a prime number?
First, sum the numbers in the frequency column to see that the experiment was performed 30 times. Then find the probabilities of the specified events.
a. Number of times 3 showed = 7
Number of tosses = 30
$P(\text{3}) = \frac{7}{30}$
b. Frequency of primes = 6 + 7 + 2 = 15
Number of trials = 30
$P(\text{prime}) = \frac{15}{30} = \frac{1}{2}$
Experimental probability can be used to predict the outcomes of experiments. This is shown in the following examples.
Example 3: The table shows the attendance schedule of an employee for the month of May.
a. What is the probability that the employee is absent?
b. How many times would we expect the employee to be present in June?
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a. The employee was absent three times and the number of days in this experiment was 31. Therefore:
$P(\text{Absent}) = \frac{3}{31}$
b. We expect the employee to be absent
$\frac{3}{31} × 30 = 2.9 ≈ 3$ days in June
Example 4: Tommy observed the color of cars owned by people in his small hometown. Of the 500 cars in town, 10 were custom colors, 100 were white, 50 were red, 120 were black, 100 were silver, 60 were blue, and 60 were grey.
a. What is the probability that a car is red?
b. If a new car is bought by someone in town, what color do you think it would be? Explain.
a. Number of red cars = 50
Total number of cars = 500
$P(\text{red car}) = \frac{50}{500} = \frac{1}{10}$
b. Based on the information provided, it is most likely that the new car will be black. This is because it has the highest frequency and the highest experimental probability.
Now it is time for you to try these examples.
The table below shows the colors of jeans in a clothing store and their respective frequencies. Use the table to answer the questions that follow.
|
|
Blue | 75 |
Black | 60 |
Grey | 45 |
Brown | 25 |
White | 20 |
- What is the probability of selecting a brown jeans?
- What is the probability of selecting a blue or a white jeans?
On a given day, a fast food restaurant notices that it sold 110 beef burgers, 60 chicken sandwiches, and 30 turkey sandwiches. From this observation, what is the experimental probability that a customer buys a beef burger?
Over a span of 20 seasons, a talent competition notices the following. Singers won 12 seasons, dancers won 2 seasons, comedians won 3 seasons, a poet won 1 season, and daring acts won the other 2 seasons.
a. What is the experimental probability of a comedian winning a season?
b. From the next 10 seasons, how many winners do you expect to be dancers?
Try this at home! Flip a coin 10 times. Record the number of tails you get. What is your P(tail)?
Number of brown jeans = 25
Total Number of jeans = 125
$P(\text{brown}) = \frac{25}{125} = \frac{1}{5}$
Number of jeans that are blue or white = 75 + 20 = 95
$P(\text{blue or white}) = \frac{95}{125} = \frac{19}{25}$
Number of beef burgers = 110
Number of burgers (or sandwiches) sold = 200
$P(\text{beef burger}) = \frac{110}{200} = \frac{11}{20}$
a. Number of comedian winners = 3
Number of seasons = 20
$P(\text{comedian}) = \frac{3}{20}$
b. First find the experimental probability that the winner is a dancer.
Number of winners that are dancers = 2
$P(\text{dancer}) = \frac{2}{20} = \frac{1}{10}$
Therefore we expect
$\frac{1}{10} × 10 = 1$ winner to be a dancer in the next 10 seasons.
To find your P(tail) in 10 trials, complete the following with the number of tails you got.
$P(\text{tail}) = \frac{\text{number of tails}}{10}$
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Experimental probability
Experimental probability (EP), also called empirical probability or relative frequency , is probability based on data collected from repeated trials.
Experimental probability formula
Let n represent the total number of trials or the number of times an experiment is done. Let p represent the number of times an event occurred while performing this experiment n times.
Example #1: A manufacturer makes 50,000 cell phones every month. After inspecting 1000 phones, the manufacturer found that 20 phones are defective. What is the probability that you will buy a phone that is defective? Predict how many phones will be defective next month.
The total number of times the experiment is conducted is n = 1000
The number of times an event occurred is p = 20
Experimental probability is performed when authorities want to know how the public feels about a matter. Since it is not possible to ask every single person in the country, they may conduct a survey by asking a sample of the entire population. This is called population sampling. Example #2 is an example of this situation.
There are about 319 million people living in the USA. Pretend that a survey of 1 million people revealed that 300,000 people think that all cars should be electric. What is the probability that someone chosen randomly does not like electric car? How many people like electric cars?
Notice that the number of people who do not like electric cars is 1000000 - 300000 = 700000
Difference between experimental probability and theoretical probability
You can argue the same thing using a die, a coin, and a spinner. We will though use a coin and a spinner to help you see the difference.
Using a coin
In theoretical probability, we say that "each outcome is equally likely " without the actual experiment. For instance, without flipping a coin, you know that the outcome could either be heads or tails. If the coin is not altered, we argue that each outcome (heads or tails) is equally likely. In other words, we are saying that in theory or (supposition, conjecture, speculation, assumption, educated guess) the probability to get heads is 50% or the probability to get tails in 50%. Since you did not actually flip the coin, you are making an assumption based on logic.
The logic is that there are 2 possible outcomes and since you are choosing 1 of the 2 outcomes, the probability is 1/2 or 50%. This is theoretical probability or guessing probability or probability based on assumption.
In the example above about flipping a coin, suppose you are looking for the probability to get a head.
Then, the number of favorable outcomes is 1 and the number of possible outcomes is 2.
In experimental probability, we want to take the guess work out of the picture, by doing the experiment to see how many times heads or teals will come up. If you flip a coin 1000 times, you might realize that it landed on heads only 400 times. In this case, the probability to get heads is only 40%.
Your experiment may not even show tails until after the 4th flip and yet in the end you ended up with more tails than heads.
If you repeat the experiment another day, you may find a completely different result. May be this time the number of heads is 600 and the number of tails is 400.
Using a spinner
Suppose a spinner has four equal-sized sections that are red, green, black, and yellow.
In theoretical probability, you will not spin the spinner. Instead, you will say that the probability to get green is one-fourth or 25%. Why 25%? The total number of outcomes is 4 and the number of favorable outcomes is 1.
1/4 = 0.25 = 25%
However, in experimental probability, you may decide to spin the spinner 50 times or even more to see how many times you will get each color.
Suppose you spin the spinner 50 times. It is quite possible that you may end up with the result shown below:
Red: 10 Green: 15 Black: 5 Yellow: 20
Now, the probability to get green is 15/50 = 0.3 = 30%
As you can see, experimental probability is based more on facts, data collected, experiment or research!
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What is Experimental Probability?
Do real life situations always work out the way your mathematical models tell you they should? No! This tutorial describes how experimental probability differs from theoretical probability.
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How Do You Find Experimental Probability?
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Probability Vocabulary
Learn words with flashcards and other activities, other learning activities, teaching tools, full list of words from this list:.
- probability a measure of how likely it is that some event will occur Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.
- distribution the act of spreading or apportioning Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions .
- outcome something that results Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.
- function what something is used for A properly normalized function that assigns a probability "density" to each possible outcome within some interval is called a probability density function (or probability distribution function), and its cumulative value (integral for a continuous distribution or sum for a discrete distribution) is called a distribution function (or cumulative distribution function).
- event something that happens at a given place and time Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.
- statistics a branch of mathematics concerned with quantitative data The analysis of events governed by probability is called statistics .
- percentage a proportion in relation to a whole In common usage, the word "probability" is used to mean the chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%.
- sum a quantity obtained by the addition of a group of numbers A properly normalized function that assigns a probability "density" to each possible outcome within some interval is called a probability density function (or probability distribution function), and its cumulative value (integral for a continuous distribution or sum for a discrete distribution) is called a distribution function (or cumulative distribution function).
- mean denote or connote In common usage, the word "probability" is used to mean the chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%.
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Probability
How likely something is to happen.
Many events can't be predicted with total certainty. The best we can say is how likely they are to happen, using the idea of probability.
Tossing a Coin
When a coin is tossed, there are two possible outcomes:
Heads (H) or Tails (T)
- the probability of the coin landing H is ½
- the probability of the coin landing T is ½
Throwing Dice
When a single die is thrown, there are six possible outcomes: 1, 2, 3, 4, 5, 6 .
The probability of any one of them is 1 6
In general:
Probability of an event happening = Number of ways it can happen Total number of outcomes
Example: the chances of rolling a "4" with a die
Number of ways it can happen: 1 (there is only 1 face with a "4" on it)
Total number of outcomes: 6 (there are 6 faces altogether)
So the probability = 1 6
Example: there are 5 marbles in a bag: 4 are blue, and 1 is red. What is the probability that a blue marble gets picked?
Number of ways it can happen: 4 (there are 4 blues)
Total number of outcomes: 5 (there are 5 marbles in total)
So the probability = 4 5 = 0.8
Probability Line
We can show probability on a Probability Line :
Probability is always between 0 and 1
Probability is Just a Guide
Probability does not tell us exactly what will happen, it is just a guide
Example: toss a coin 100 times, how many Heads will come up?
Probability says that heads have a ½ chance, so we can expect 50 Heads .
But when we actually try it we might get 48 heads, or 55 heads ... or anything really, but in most cases it will be a number near 50.
Learn more at Probability Index .
Some words have special meaning in Probability:
Experiment : a repeatable procedure with a set of possible results.
Example: Throwing dice
We can throw the dice again and again, so it is repeatable.
The set of possible results from any single throw is {1, 2, 3, 4, 5, 6}
Outcome: A possible result.
Example: "6" is one of the outcomes of a throw of a die.
Trial: A single performance of an experiment.
Example: I conducted a coin toss experiment. After 4 trials I got these results:
| Trial | Trial | Trial | Trial | |
|---|---|---|---|---|
| Head | ✔ | ✔ | ✔ | |
| Tail | ✔ |
Three trials had the outcome "Head", and one trial had the outcome "Tail"
Sample Space: all the possible outcomes of an experiment.
Example: choosing a card from a deck
There are 52 cards in a deck (not including Jokers)
So the Sample Space is all 52 possible cards : {Ace of Hearts, 2 of Hearts, etc... }
The Sample Space is made up of Sample Points:
Sample Point: just one of the possible outcomes
Example: Deck of Cards
- the 5 of Clubs is a sample point
- the King of Hearts is a sample point
"King" is not a sample point. There are 4 Kings, so that is 4 different sample points.
There are 6 different sample points in that sample space.
Event: one or more outcomes of an experiment
Example Events:
An event can be just one outcome:
- Getting a Tail when tossing a coin
- Rolling a "5"
An event can include more than one outcome:
- Choosing a "King" from a deck of cards (any of the 4 Kings)
- Rolling an "even number" (2, 4 or 6)
Hey, let's use those words, so you get used to them:
Example: Alex wants to see how many times a "double" comes up when throwing 2 dice.
The Sample Space is all possible Outcomes (36 Sample Points):
{1,1} {1,2} {1,3} {1,4} ... ... ... {6,3} {6,4} {6,5} {6,6}
The Event Alex is looking for is a "double", where both dice have the same number. It is made up of these 6 Sample Points :
{1,1} {2,2} {3,3} {4,4} {5,5} and {6,6}
These are Alex's Results:
| Trial | Is it a Double? |
|---|---|
| {3,4} | No |
| {5,1} | No |
| {2,2} | |
| {6,3} | No |
| ... | ... |
After 100 Trials , Alex has 19 "double" Events ... is that close to what you would expect?
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COMMENTS
Probability. A number from 0 to 1 (or 0% to 100%) that describes how likely an event is to occur. Compound event. An event made up of two or more simple events. Experimental Probability. The ratio of the number of times an event occurs to the total number of trials, or times that the activity is performed. Theoretical Probability.
Experimental Probability: Examples. Let's take a look at some of the examples of experimental probability. Example 1: Ben tried to toss a ping-pong ball in a cup using 10 trials, out of which he succeeded 4 times. P (win) = N u m b e r o f s u c c e s s N u m b e r o f t r i a l s. = 4 10. = 2 5.
Outcome. a possible result. Probability. a number between 0 and 1 that describes the likelihood an event will occur. Random. a process of selection in which each item of a set has an equal chance of being selected. Theoretical Probability. probability that shows what should happen under ideal circumstances.
the number of ways that the event can occur, divided by the total number of outcomes. Experimental Probability. an "estimate" that the event will happen based on how often the event occurs after collecting data or running an experiment (with a large number of trials). It is based specifically on direct observations or experiences.
The experimental probability of an event is based on the number of times the event has occurred during the experiment and the total number of times the experiment was conducted. Each possible outcome is uncertain and the set of all the possible outcomes is called the sample space. The formula to calculate the experimental probability is: P (E ...
Random experiments are repeated multiple times to determine their likelihood. An experiment is repeated a fixed number of times and each repetition is known as a trial. Mathematically, the formula for the experimental probability is defined by; Probability of an Event P (E) = Number of times an event occurs / Total number of trials.
Number of tosses = 30. P (3) = 7 30. b. Frequency of primes = 6 + 7 + 2 = 15. Number of trials = 30. P (prime) = 15 30 = 1 2. Experimental probability can be used to predict the outcomes of experiments. This is shown in the following examples. Example 3: The table shows the attendance schedule of an employee for the month of May.
Definition: Probability. The probability of any outcome is the long-term relative frequency of that outcome. Probabilities are between zero and one, inclusive (that is, zero and one and all numbers between these values). P(A) = 0 P (A) = 0. means the event A A.
Experimental probability (EP), also called empirical probability or relative frequency, is probability based on data collected from repeated trials. Experimental probability formula. Let n represent the total number of trials or the number of times an experiment is done. Let p represent the number of times an event occurred while performing ...
The experimental probability is the number of times the event occurred divided by the total number of trials. If there are 10 trials, and an even number is chosen 6 times, then we have: [Math Processing Error] P (e v e n) = 6 10 = 3 5 = 60 %. The theoretical probability is 40% and the experimental probability is 60%.
This is a combination of the four simple events of rolling a 1, rolling a 2, rolling a 3, and rolling a 4 combined. • Probability of flipping two coins and getting at least one head. There are three possible answers in the sample space { (H,H), (H,T) (T,H) }. Don't confuse "experiment" with "event"! We think of "events" as big happenings ...
Term. Definition. experimental probability. Experimental (empirical) probability is the actual probability of an event resulting from an experiment. theoretical probability. Theoretical probability is the probability ration of the number of favourable outcomes divided by the number of possible outcomes. Image Attributions.
A form of theoretical probability determined by a ratio of lengths, areas, or volumes. Each repetition of an experiment. The ratio of the number of times that the event occurs, the frequency, to the number of trials. Study with Quizlet and memorize flashcards containing terms like Probability, Outcome, Sample Space and more.
How Do You Find Experimental Probability? Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. In this non-linear system, users are free to take whatever path through the material best serves their needs.
Vocabulary ; Writing & Composition Health & Medicine Counseling & Therapy ... Experimental probability is the ratio of the number of times an outcome occurs to the total number of times the ...
Vocabulary Language: English English; Term Definition; experimental probability: Experimental (empirical) probability is the actual probability of an event resulting from an experiment. Favorable Outcome: A favorable outcome is the outcome that you are looking for in an experiment.
Go outside to that basketball court and shot ten 3-pointer shots (shots beyond the 3-point arc) and record how many baskets you make. This is your experimental probability! Set up a ratio of the number of 3-point shots that you made compared to 10, the total number of trails in your experiment. Set up that ratio as a fraction, and reduce it.
The set of all possible outcomes. Probability of an event. The relative frequency of the event, when the experiment is performed many many times. Assuming the coin is fair, each of the outcomes will occur roughly the same number of times in many repeats of the experiment. The probability of "two tails" will be 3/8.
probability. tells you how likely it is that the event will occur. theoretical probability. p (event)= number of favorable outcomes/number of possible outcomes. complement of an event. consists of all outcomes in the sample space that are not in the event. experimental probability. p (event) = number of times the event occurs/number of times ...
Probability and Expected Value Vocabulary Term Definition Diagrams/Example Probability times. A number between 0 and 1 that describes the likelihood that an outcome will occur. The probability of a certainoutcome is 1, while the probability of an impossible outcome is 0. When a fair number cube is rolled, 2 can be expected ⅙ Experimental ...
a proportion in relation to a whole. In common usage, the word "probability" is used to mean the chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%. sum. a quantity obtained by the addition of a group of numbers.
Many events can't be predicted with total certainty. The best we can say is how likely they are to happen, using the idea of probability. Tossing a Coin. When a coin is tossed, there are two possible outcomes: Heads (H) or Tails (T) Also: the probability of the coin landing H is ½; the probability of the coin landing T is ½ . Throwing Dice
Math Basic Probability Vocabulary. Term. 1 / 17. Probability. Click the card to flip 👆. Definition. 1 / 17. A number that describes how likely an event is to occur. Click the card to flip 👆.