Q. 14 4.4( 32 Votes )

Probability of solving specific problem independently by A and B are 1/2 and 1/3 respectively. If both try to solve the problem independently, find the probability that

(i) the problem is solved (ii) exactly one of them solves the problem.

Answer :

Given:

P(A) = Probability of solving the problem by A = 1/2


P(B) = Probability of solving the problem by B = 1/3


Because A and B both are independent.


P (A B) = P(A) . P(B)


P (A B) =


P(A) = 1 – P(A) = 1 – 1/2 = 1/2


P(B) = 1 – P(B) =


(i) the problem is solved


The problem is solved, i.e. it is either solved by A or it is solved by B.


= P(A B)


As we know, P (A B) = P(A) + P(B) - P (A B)


P (A B) =



(ii) exactly one of them solves the problem


i.e. either problem is solved by A but not by B or vice versa


i.e. P(A).P(B) + P(A).P(B)


=


=


P(A).P(B) + P(A).P(B) = 1/2


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