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.

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`