Find the conditional probability of the indicated event when two fair dice (one

Question

Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. HINT [See Example 1.] The red one is 6, given that the sum is 9. Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. HINT [See Example 1.] The red one is 6, given that the sum is 9. Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. HINT [See Example 1.] The red one is 6, given that the sum is 9.

Explanation / Answer

Probability that red dice shows 6, P(R6) = 1/6
Probability that sum of two dice is 9, P(sum 9) = 4/36

Probability that red dice shows 6 and sum of two dice is 9, P(R6 and sum 9) = 2/36 = 1/18

Required probability, P(R6 | sum 9) = P(R6 and sum 9) / P(sum 9) = 2/4 = 1/2 = 0.5

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