a pair of dice is rolled. is the event of rolling a sum of the dice is an odd number. Find the probability that the sum is a five or a ten, given that an odd sum is rolled.

Answer 1

The notation for conditional probability is P(B|A), read as the probability of B given A.
P(B|A) = P(A and B)/P(A)

for yours P(A) = P(odd sum is rolled)
P(B) = P(5 or 10)

ways to get 5: (1,4) (2,3) (3,2) (4,1) --> 4 ways
ways to get 10: (4,6) (5,5) (6,4) -- > 3 ways

P(A) = 18/36 = 1/2

P(A and B) = P((5or10) and odd) = 4/36

P(B|A) (4/36)/(1/2) = 2/9