Question

Suppose that Eitan rolls a fair six-sided die and a fair four-sided die simultaneously. Let A be the event that the sum of the dice is 8 and B be the event that Eitan rolls doubles. Using a sample space of the possible outcomes, answer each of the following questions.

a. What is P(A), the probability that the sum of the dice is 8?
b. What is P(B), the probability that Eitan rolls doubles?
c. What is P(A and B), the probability that the sum of the dice is 8 and Eitan rolls doubles?
d. Are events A and B independent? (Choose 1 answer):
a1. Yes, events A and B are independent
b1. No, events A and B are not independent events

Answer 1

event that Eitan rolls doubles. Using a sample space of the possible outcomes, answer each of the following questions.

a

Answer 2

Explanation:

Part A

Let's see what the total ways of eight might be.

Dice (6 sides) Dice (4 sided)

6 2 You can't reverse them

5 3 You can't reverse these either.

4 4 You can't have a meaningful reversal.

That looks like all there is. So what's the universe of this set?

6 * 4 is the total number of combinations.

You have 3 that work.

P(A) = 3/24 = 1/8 = 0.125

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Part B

There are 4 sets of doubles. As you can see, there is not 2 creations, so the answer is

P(B) = 4/24 = 1/6 = 0.1667

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Part C

P(A + B) = only 1 instance (4,4)

1/24 = 0.04167

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No they are not independent. They can both happen.