The conditional probability that the first die shows 4, given that the sum of the three numbers showing is 12 is 1/6 .
Given :
Suppose we roll three fair six-sided dice. Compute the conditional probability that the first die shows 4, given that the sum of the three numbers showing is 12 .
Probability of p ( die 1 = 4 | sum 3 = 12 ) = p ( die 1 = 4 and sum 3 = 12 ) / p ( sum 3 = 12 )
= 1/6 * 1/6 / 6 / 36
= 1 * 1 / 6 * 6 / 6 / 36
= 1 / 36 / 6 / 36
= 1 / 36 / 6 / 36
= 1 / 1 / 6 / 1
= 1 * 1 / 6 * 1
= 1/6
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