Refer to the following information for Questions 6 7 and 8 S

Refer to the following information for Questions 6, 7, and 8. Show all work. Just the answer, without supporting work, will receive no credit.
A fair 6-faced die is rolled two times. Let A be the event that the outcome of the first roll is a multiple of 3, and B be the event that the outcome of second roll is greater than 4.
6. How many outcomes are there in the sample space? (5 pts)
7. What is the probability that the outcome of the second roll is greater than 4, given that the first roll is a multiple of 3?

Solution

6) Sample space consists of 36 as follows:

(1,1)(1,2)...(1,6)

(2,1) (2,2)...(2,6)

...

(3,1)(3,2)...(3,6)

7) P(A) = 2/6 and P(B) = 2/6

P(AB) = 1/6

As 6 is common for A and B

P(B/A) =P(AB)/P(A) = 1/6 / 2/6 = 0.5