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

Question

2592 views around the world

You can reuse this answer
Creative Commons License

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#