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Probabilities of solving a specific problemindependently by A and B are`1/2 a n d1/3`respectively. Ifboth try to solve the problem independently, find the probability that (i)the problem is solved (ii) exactly one of them solves the problem. |
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Answer» Let `P(A)` is the probability that `A` solves the problem and `P(B)` is the probability that `B` solves the problem. Here, `P(A) = 1/2 and P(B) = 1/3` `:. P(barA) = 1-1/2 = 1/2` `P(barB) = 1-1/3 = 2/3` (i) Probability when the problem is solved: In this case either one of them or both of them can solve the problem. So, required probability, `=P(A)P(barB)+P(B)P(barA)+P(A)P(B)` `=1/2*2/3+1/3*1/2+1/2*1/3 = 1/3+1/6+1/6 ` `=2/3.` (ii) Probability when exactly one of them solve the problem : In this case, required probability `= P(A)P(barB)+P(B)P(barA)` `=1/2*2/3+1/3*1/2 = 1/3+1/6` `=1/2.` |
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