Question

You roll two dice. Let A be the event that the sum of the dice is an even number. Let B be the event that the two results are different. If B has occured, what is the proability A has also occured?

Answer 1

total number of events =6*6=36

number of events that two rolls are same =6 ; {(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}
therefore events in B =36-6 =30

hence probability of B =P(B) =30/36 =5/6

events where two rolls are different and sum is even =number of ways first roll is odd and second is odd+first is even and second is even =3*2+3*2=12

terefore probability that rolls are different and sum is even =P(AnB) =12/36 =1/3

hence proability A has also occured given B has occured =P(AnB)/P(B) =(1/3)/(5/6) =2/5