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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.
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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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11.2.1.2- cards (equal proportions), example: cards section .
Research question : When randomly selecting a card from a deck with replacement, are we equally likely to select a heart, diamond, spade, and club?
I randomly selected a card from a standard deck 40 times with replacement. I pulled 13 hearts, 8 diamonds, 8 spades, and 11 clubs.
Let's use the five-step hypothesis testing procedure:
\(H_0: p_h=p_d=p_s=p_c=0.25\) \(H_a:\) at least one \(p_i\) is not as specified in the null
We can use the null hypothesis to check the assumption that all expected counts are at least 5.
\(Expected\;count=n (p_i)\)
All \(p_i\) are 0.25. \(40(0.25)=10\), thus this assumption is met and we can approximate the sampling distribution using the chi-square distribution.
\(\chi^2=\sum \dfrac{(Observed-Expected)^2}{Expected} \)
All expected values are 10. Our observed values were 13, 8, 8, and 11.
\(\chi^2=\dfrac{(13-10)^2}{10}+\dfrac{(8-10)^2}{10}+\dfrac{(8-10)^2}{10}+\dfrac{(11-10)^2}{10}\) \(\chi^2=\dfrac{9}{10}+\dfrac{4}{10}+\dfrac{4}{10}+\dfrac{1}{10}\) \(\chi^2=1.8\)
Our sampling distribution will be a chi-square distribution.
\(df=k-1=4-1=3\)
We can find the p-value by constructing a chi-square distribution with 3 degrees of freedom to find the area to the right of \(\chi^2=1.8\)
The p-value is 0.614935
\(p>0.05\) therefore we fail to reject the null hypothesis.
There is not enough evidence to state that the proportion of hearts, diamonds, spades, and clubs that are randomly drawn from this deck are different.
IMAGES
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1 Calculate the experimental probability of selecting a heart by dividing the number of times a heart was selected by the total number of trials. If Amanda selected a heart 9 times out of 30 trials, the experimental probability is 9 30 \frac{9}{30} 30 9
Probability Worksheet 4 p.1 Revised June 2010 Experimental and Theoretical Probability Name _____ Per ____ Date _____ Amanda used a standard deck of 52 cards and selected a card at random. She recorded the suit of the card she picked, and then replaced the card. The results are in the table below. Diamonds
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1 Calculate the experimental probability of selecting a heart by dividing the number of times a heart was selected by the total number of trials. Let's assume the number of times a heart was selected is 9 and the total number of trials is 52. Therefore, the experimental probability is 9 52 \frac{9}{52} 52 9
Stanley picks a card from a standard deck of cards and gets heart. He returns the card to the deck, picks a second time, and gets another heart. Stanley repeats this process a total of five times and gets a heart in four of those trials. Should Stanley conclude that the probability of selecting a heart is \(\frac{4}{5} = 0.80 = 80\%\)?
Experimental Probability Worksheet Show your work/ Per: # on Cube Frequency Thl: I.) What is the theoretical probability that an even number will ... What is the theoretical pggþgži_lLty of selecting a heart? c.) Based on her results, what i the experimentql probability of selecting a diamond or a spade? 19 11 30
The formula for calculating experimental probability is: P (E) = Number of times event E occurs / Total number of trials. For example, if you roll a dice 60 times, and the number 4 comes up 15 times, the experimental probability of rolling a 4 is calculated as 15 (the number of times 4 occurs) divided by 60 (the total number of trials), which ...
What is the experimental probability of selecting a heart? Leave your answer as a percent to the nearest tenth (one decimal) after converting to %. You can leave out the % sign. Diana selects one card at a time 3 0 times from a deck of 5 2 cards. She selects a heart 9 times. What is the experimental probability of selecting a ...
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.
Step 3: Determine the p-value. Our sampling distribution will be a chi-square distribution. d f = k − 1 = 4 − 1 = 3. We can find the p-value by constructing a chi-square distribution with 3 degrees of freedom to find the area to the right of χ 2 = 1.8. The p-value is 0.614935. Step 4: Make a decision.
If you select one card from a standard, 52-card deck, the probability that you pull a heart is ¼ (25%), right? With 13 cards of each suit in a 52-card deck, exactly one fourth of those cards are hearts. ... what is the experimental probability of selecting a diamond or a spade? d. What is the theoretical probability of selecting a diamond or a ...
Using a standard deck of 52 cards, Lisa drew a card, recorded the suit of the card picked, then replaced it back in the deck. She continued this for a total of 40 draws. The table shows the frequency of each type of card drawn. Determine the experimental probability of not selecting a heart. (2 points)
Compare these results, and describe your findings.15) Dale conducted a survey of the students in hi. lasses to observe the distribution of eye. B. eBrownGreenHazelNumber125828a.) Find the experi. l probability distribution for each eye color. P(blue)= _______ P(. row.
1 Calculate the experimental probability of getting a heart. The correct answer is P ( h e a r t ) = 9 52 P(heart) = \frac{9}{52} P ( h e a r t ) = 52 9 , which corresponds to option B 2 Determine the experimental probability of getting a club.
Final answer: To find the experimental probability of not selecting a heart, we calculate the number of cards that are not hearts and divide it by the total number of draws.In this case, the probability is 100%. Explanation: To determine the experimental probability of not selecting a heart, we need to find the total number of cards that are not hearts and divide it by the total number of draws.
How does the experimental probability of choosing a heart compare with the theoretical probability of choosing a heart? A.The theoretical probability of choosing a heart is 1/16 greater than the experimental probability of choosing a heart. B.The experimental probability of choosing a heart is 1/16 greater than the theoretical probability of ...
The table shows the frequency of each type of card drawn. Using a standard deck of 52 cards, Lisa drew a card, recorded the suit of the card picked, then replaced it back in the deck. She continued this for a total of 40 draws. The table shows the frequency of each type of card drawn. There are 2 steps to solve this one.
She recorded the suit of each card she picked, then replaced the cahe results are in the table below. Use the table to answer #2-6. 2. What is the experimental probability of selecting a heart? 1/52 3. What is the theoretical probability of selecting a heart? 13/52 4. What is the experimental probability of selecting a diamond?
The correct option is (D) P(not heart) = 77.5%. The experimental probability of not selecting a heart is P(not heart) = 77.5%. Let's denote the number of times a heart was not drawn as N(not heart). According to the table provided in the question, we would have the total number of draws (which is 40) and the number of times each suit was drawn.
1 Calculate the probability of drawing a heart by dividing the frequency of hearts by the total number of draws. Since there were 9 hearts out of 40 draws, ... Therefore, the experimental probability of not selecting a heart is 77.5 % 77.5\% 77.5%. Helpful. Not Helpful. Gauth it, Ace it! [email protected]. Company.
The experimental probability of not selecting a heart is (D)P(not heart) = 77.5%. How to find the experimental probability ? The experimental probability that a heart is selected is: = Number of times hearts was selected / Number of times Lisa drew a card = 9 / 40 . This then means that the experimental probability of not selecting a heart is: = 1 - experimental probability of selecting a heart
The results are in the table below. 1. Based on her results, what is the experimental probability of selecting a heart? 2. What is the theoretical probability of selecting a heart? 3. Based on her results, what is the experimental probability of selecting a diamond or a spade? 4. What is the theoretical probability of selecting a diamond or a ...