Q. 183.7( 3 Votes )

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

Answer :

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, =


(answer)


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