Q. 205.0( 2 Votes )

A die is thrown twice, and the sum of the numbers appearing is observed to be 8 What is the conditional probability that the number 5 has appeared at least once?

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 5 has appeared once =


= {(1,5),(2,5),(3,5),(4,5),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,5)} =11


Hence P(B) =


(A B) = outcomes of getting sum as 8 with at least one die showing 5


= {(3,5),(5,3)= 2


Hence P(A B)


Therefore, =


(answer)


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