Which of the following statements best describes the relationship between experimental and theoretical probabilities?
Responses
A Experimental and theoretical probabilities can be close, but they can never be exactly equal.Experimental and theoretical probabilities can be close, but they can never be exactly equal.
B As the number of trials decreases, the experimental probability should get closer to the theoretical probability.As the number of trials decreases, the experimental probability should get closer to the theoretical probability.
C As the number of trials increases, the experimental probability should get closer to the theoretical probability.As the number of trials increases, the experimental probability should get closer to the theoretical probability.
D As the theoretical probability increases, the experimental probability should get closer to the theoretical probability.As the theoretical probability increases, the experimental probability should get closer to the theoretical probability.
11 answers
C As the number of trials increases, the experimental probability should get closer to the theoretical probability.
Luis has 3 red marbles, 5 blue marbles, 4 yellow marbles, and 8 black marbles in a bag. He records the color marble he pulls from the bag and puts the marble back in the bag 14 times. The table below shows the frequency he pulled each color.
What are the experimental and theoretical probability of pulling a yellow marble out of the bag? Round your answer to the nearest hundredth.
red:2
blue:4
yellow:2
black:6
Experimental probability
Theoretical probability
What are the experimental and theoretical probability of pulling a yellow marble out of the bag? Round your answer to the nearest hundredth.
red:2
blue:4
yellow:2
black:6
Experimental probability
Theoretical probability
To find the experimental probability of pulling a yellow marble, you add up the frequency of pulling a yellow marble and divide it by the total number of trials. In this case, the frequency of pulling a yellow marble is 2 out of 14 trials.
Experimental probability of pulling a yellow marble = 2/14 ≈ 0.14
To find the theoretical probability of pulling a yellow marble, you divide the number of yellow marbles by the total number of marbles in the bag.
Total number of marbles = 3 + 5 + 4 + 8 = 20
Number of yellow marbles = 4
Theoretical probability of pulling a yellow marble = 4/20 = 0.20
Therefore, the experimental probability of pulling a yellow marble is approximately 0.14 and the theoretical probability is 0.20.
Experimental probability of pulling a yellow marble = 2/14 ≈ 0.14
To find the theoretical probability of pulling a yellow marble, you divide the number of yellow marbles by the total number of marbles in the bag.
Total number of marbles = 3 + 5 + 4 + 8 = 20
Number of yellow marbles = 4
Theoretical probability of pulling a yellow marble = 4/20 = 0.20
Therefore, the experimental probability of pulling a yellow marble is approximately 0.14 and the theoretical probability is 0.20.
How much pizza sauce is needed to cover a 16" pizza? (Note: 16" is the diameter of the pizza.)
Responses
A 50.24
50.24 in 2
B 200.96
200.96 in 2
C 803.84
803.84 in 2
D 3215.36
Responses
A 50.24
50.24 in 2
B 200.96
200.96 in 2
C 803.84
803.84 in 2
D 3215.36
To calculate the amount of sauce needed to cover a 16" pizza, you would use the formula for the area of a circle, which is A = πr^2, where r is the radius of the circle and π is approximately 3.14159.
Given that the diameter of the pizza is 16", the radius (r) would be half of the diameter, so r = 16"/2 = 8".
Plugging in the radius into the formula:
A = π(8)^2 ≈ 3.14159 * 64 ≈ 200.96 in^2
Therefore, the amount of pizza sauce needed to cover a 16" pizza is approximately 200.96 in^2.
The correct answer is B) 200.96 in^2.
Given that the diameter of the pizza is 16", the radius (r) would be half of the diameter, so r = 16"/2 = 8".
Plugging in the radius into the formula:
A = π(8)^2 ≈ 3.14159 * 64 ≈ 200.96 in^2
Therefore, the amount of pizza sauce needed to cover a 16" pizza is approximately 200.96 in^2.
The correct answer is B) 200.96 in^2.
There are three choices of fruit are bananas, pears, and oranges. If the probability of getting a banana is 5/12 and the probability of getting a pear is 1/6, what is the probability of getting an orange?
Responses
A 5/12
b 1/2
C 1/3
D 1/12
Responses
A 5/12
b 1/2
C 1/3
D 1/12
If the probabilities of getting a banana and a pear are given as 5/12 and 1/6 respectively, and these are the only three choices, then the sum of the probabilities of getting a banana, pear, and orange should add up to 1 (since these are the only possible outcomes).
Let x be the probability of getting an orange.
So, 5/12 + 1/6 + x = 1
Multiplying by 12 to clear fractions, we get:
5 + 2 + 12x = 12
7 + 12x = 12
12x = 5
x = 5/12
Therefore, the probability of getting an orange is 5/12.
The correct answer is A) 5/12.
Let x be the probability of getting an orange.
So, 5/12 + 1/6 + x = 1
Multiplying by 12 to clear fractions, we get:
5 + 2 + 12x = 12
7 + 12x = 12
12x = 5
x = 5/12
Therefore, the probability of getting an orange is 5/12.
The correct answer is A) 5/12.
Which describes a non-uniform probability model?
Responses
A selecting a single card from a deck of cardsselecting a single card from a deck of cards
B selecting a ball from 2 purple balls and 2 green ballsselecting a ball from 2 purple balls and 2 green balls
C the chance of an odd or even number from rolling a diethe chance of an odd or even number from rolling a die
D selecting a day of the week using only the first letter of that day
Responses
A selecting a single card from a deck of cardsselecting a single card from a deck of cards
B selecting a ball from 2 purple balls and 2 green ballsselecting a ball from 2 purple balls and 2 green balls
C the chance of an odd or even number from rolling a diethe chance of an odd or even number from rolling a die
D selecting a day of the week using only the first letter of that day
D selecting a day of the week using only the first letter of that day.
In a non-uniform probability model, the outcomes do not have equal probabilities. In the case of selecting a day of the week using only the first letter of that day, the probability of selecting a specific day would depend on how many days start with the same letter. This results in a non-uniform probability model.
In a non-uniform probability model, the outcomes do not have equal probabilities. In the case of selecting a day of the week using only the first letter of that day, the probability of selecting a specific day would depend on how many days start with the same letter. This results in a non-uniform probability model.
The table shows the results of randomly selecting colored marbles from a bag 36 times. The marble was returned to the bag after each selection.
White Red Black Blue
Number of
Times
Selected 8 14 9 5
Based on these results, what is the expected probability of randomly selecting a black marble from the bag in one attempt?
Responses
A 0.1390.139
B 0.220.22
C 0.250.25
D 0.90.9
White Red Black Blue
Number of
Times
Selected 8 14 9 5
Based on these results, what is the expected probability of randomly selecting a black marble from the bag in one attempt?
Responses
A 0.1390.139
B 0.220.22
C 0.250.25
D 0.90.9
To find the expected probability of randomly selecting a black marble from the bag in one attempt, you need to calculate the total number of selections and the number of times a black marble was selected.
Total number of selections = 8 (white) + 14 (red) + 9 (black) + 5 (blue) = 36
Number of times a black marble was selected = 9
Expected probability = Number of times black marble was selected / Total number of selections
Expected probability = 9 / 36 = 0.25
Therefore, the expected probability of randomly selecting a black marble from the bag in one attempt is 0.25.
The correct answer is C) 0.25.
Total number of selections = 8 (white) + 14 (red) + 9 (black) + 5 (blue) = 36
Number of times a black marble was selected = 9
Expected probability = Number of times black marble was selected / Total number of selections
Expected probability = 9 / 36 = 0.25
Therefore, the expected probability of randomly selecting a black marble from the bag in one attempt is 0.25.
The correct answer is C) 0.25.
5 answers