What is the probability that the sum of two dice rolls is 12 if the sum is even?

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Answer 1 · 2015-10-25T16:07:05

The probability is $P (A / B) = \frac{1}{18}$ $P(A//B)=1/18$

If we denote:

$A$ $A$ - the sum of 2 dice is $12$ $12$
$B$ $B$ - the sum of 2 dice is even

Then we are looking for a conditional probability $P (A / B)$ $P(A//B)$
According to the definition we are looking for:

$P (A / B) = \frac{P (A \cap B)}{P (B)}$ $P(A//B)=(P(AnnB))/(P(B))$

$|Omega|=36$

$AnnB={(6;6)}$

$|AnnB|=1$
$P(AnnB)=1/36$

$B={(1,1);(1,3);(1,5);(2,2);(2,4);(2;6),(3,1);(3,3);(3,5);(4;2);(4,4);(4,6);(5,1);(5,3);(5,5);(6,2);(6,4);(6,6)}$

$|B|=18$
$P(B)=18/36=1/2$

$P(A//B)=1/36:1/2=1/36*2=1/18$