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)=1/18#

If we denote:

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

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

#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#