# Multiplication Rule

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## Multiplication Rule Answer Key

1.

Given that P(A) = 0.31, P(A|B) = 0.48, and P(B|A) = 0.15, what is P(B)?

- 0.48
- 0.23
- 0.99
- 0.10

2.

Given that P(A) = 0.61, P(B) = 0.33, and P(A|B) = 0.09, what is P(B|A)?

- 0.17
- 0.05
- 0.27
- 0.20

3.

Given that P(A and B) = 0.14, P(A) = 0.55, and P(B) > P(B|A), what is P(A|B)?

- 0.25
- 0.08
- 0.55
- Not enough information.

4.

Given that P(A) = 0.71, P(B) = 0.22, and P(A|B) = 0.13, what is P(A and B)?

- 0.03
- 0.04
- 0.09
- 0.42

5.

A regular set of billiard balls has 15 balls, with the numbers 1-15 on them. The first eight balls (1-8) are solid, and are the colors yellow, blue, red, purple, orange, green, maroon, and black respectively. The next seven balls (9-15) are striped (white with a stripe of color), the colors being the same as for the solid (9 being yellow striped, 10 being blue striped, etc), but no black. If there is a set of billiard balls in a box, what is the probability that you pick out a blue ball, given that it is a striped ball?

- 1/15
- 2/15
- 1/2
- 1/7

6.

Given a 12-sided die, with the numbers 1 through 12 on the sides, what is the probability that a multiple of 2 is rolled, given that the roll is a factor of 36?

- 1/2
- 4/7
- 2/3
- 1/3

7.

Given a 12-sided die, with the numbers 1 through 12 on the sides, what is the probability that a prime number is rolled, given that the roll is a factor of 60? Choose the answer that correctly represents this.

- [math](1/4)/(3/8)[/math]
- [math](1/4)/ (5/12)[/math]
- [math](3/5 * 5/12) / (2/3)[/math]
- [math](3/8 * 2/3) / (5/12) [/math]

8.

A standard deck of cards has 52 cards. Let F be the event that a red face card is drawn (a jack, queen, or king of diamonds or hearts), and let D be the event that a diamond is drawn. If a card is drawn randomly from the deck, which of the following are correct applications of the general Multiplication Rule? Choose all correct answers.

- [math] P(F and D) = 1/2 * 3/26 [/math]
- [math] P(F|D) = (3/26 * 1/2)/(1/4) [/math]
- [math]P(D|F) = (3/52)/(3/26)[/math]
- [math]P(D) = (1/2 * 3/26)/(3/13) [/math]

9.

There are 26 students in Mr. Hinthorne's class. There are 12 male students. Of the male students, 3 wear glasses. 6 of the female students wear glasses. Let G represent choosing a person with glasses and F a female student. Which of the following are correct applications of the Multiplication Rule? Choose all that apply.

- [math]P(F) = (9/26 * 3/7)/(2/3) [/math]
- [math]P(F|G) = (7/13 * 3/7)/(9/26)[/math]
- [math]P(F and G) = 7/13 * 9/26[/math]
- [math]P(G|F) = (3/13) / (7/13)[/math]

10.

At Monarch Collegiate Institute, a survey was conducted about the number of students who play rugby and the number of students who read science fiction books. Let R be the event that a student plays rugby, and S be the event that a student reads science fiction books. If there were 60 students surveyed, P(R|S) = 5/7, P(S|R) = 1/3, and P(S) = 7/60, which of the following expressions gives the number of students who said they play rugby and why? Choose all correct answers.

- [math]60 ( (7/60 * 5/7) / (1/3) ) [/math], by applying the general Multiplication Rule to find P(R), then multiplying by 60.
- [math]60 (1 - 7/60 + (7/60 * 5/7)) [/math], since it can assumed that everyone who doesn't read science fiction plays rugby. Therefore, subtract P(S) from one, but add back in P(S and R) (found using the general Multiplication Rule), and then multiply by 60.
- [math] 7/60 * 1/3 = 7/180 = "P(S and R)", \ \ \ 60 ( (7/180) / (5/7) )[/math], by applying the general Multiplication Rule to find P(S and R), then using it again to find P(R) and then multiplying by 60.
- Not possible. If 60 is multiplied by 5/7 (the conditional probability of choosing someone who plays rugby, given that they read science fiction), the number is not a whole number. This means that either the total number of participants or this probability is incorrect.

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