Question

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. Select the correct answer from above options

Answer 1

Here, `P(A) = 1/2` `P(B) = 1/3` `P(AnnB) = 1/2**1/3 = 1/6` Probablity that problem will be solved, `P(AuuB) = P(A)+P(B)-P(AnnB)` `=1/2+1/3-1/6 = (3+2-1)/6 = 4/6 = 2/3` Probablity exactly one of them will solve the problem = Probablity either of them solve the problem `- `Probablity both of them solve the problem =`P(AuuB)-P(AnnB) `= `2/3-1/6 = 3/6 = 1/2`