# Find the probability that the sum of the numbers showing on two dice is 8, given that least one die does not show five.

We know, when a pair of dice is thrown, total possible outcomes are = 36

A=No of outcomes for getting sum of 8 are

{(2,6),(3,5),(4,4),(5,3),(6,2)} = 5

Therefore, P(A) =

B= No of outcomes for at least one die does not show 5

= {(1,1),(1,2),(1,3),(1,4),(1,6),(2,1),(2,2),(2,3),(2,4),(2,6),(3,1),(3,2),(3,3),(3,4),(3,6),(4,1),(4,2),

(4,3),(4,4),(4,6),(6,1),(6,2),(6,3),(6,4),(6,6) } = 25

Hence P(B) =

(A B) = outcomes of getting sum as 8 with at least one die not showing 5

= {(2,6),(4,4),(6,2)= 3

Hence P(A B) =

Therefore, =

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