Question

if two faire dice are rolled, find the probability that

a) the roll is a double given that the sum is less than 5

b) the roll is a double given that the sum is 11

Answer 1

If two fair dice are rolled,

(a) Number of possible outcomes of  the sum is less than 5 are 6

i.e. (1,1),(1,2),(1,3),(2,1),(2,2),(3,1)

Number of favorable outcomes of  the roll is a double are 2

i.e. (1,1),(2,2)

The probability that  the roll is a double given that the sum is less than 5 is

(b) Number of possible outcomes of  the sum is 11 are 2

i.e. (5,6),(6,5)

Number of favorable outcomes of  the roll is a double are 0

  The probability that the roll is a double given that the sum is 11 is