A) Find the conditional probability of the indicated event when two fair dice (o

Question

A) Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled.

The red one is 6, given that the sum is 10.

B) Use the counting techniques from the last chapter. A bag contains three red marbles, four green ones, one fluorescent pink one, two yellow ones, and three orange ones. Suzan grabs four at random. Find the probability of the indicated event.

She gets one of each color other than fluorescent pink, given that she gets the fluorescent pink one.

Explanation / Answer

A)

P(sum is 10) = P(A) = 3/36

P(sum is 10 and 6 on red) = P(A and B) = 1/36

=> required probability = P(B/A) = P(A and B)/P(A) = (1/36)/(3/36) = 1/3

B)

P(A) =  12C4/13C4

P(A and B) = 3 x 4 x 2 x 3/13C4 = 72/13C4

P(B/A) = 72/12C4 = 72 x 4 x 3 x 2/(12 x 11 x 10 x 9) = 6 x 4 x 3 x 2/(11 x 10 x 3 x 3) = 2 x 4 x 2/(110) = 16/110

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