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

N/a

Explanation

Probability that A can solve the problem,
`P(A)=1/2`
Probability that B can solve the problem `P(B)=1/3`
Probability that A cannot solve the problem
`P(A')=1-P(A)=1-1/2=1/2`
and probability that B cannot solve the problem,
`P(B')=1-P(B)=1-1/3=2/3`
(i) `P` (problem is solved)
`=1-P` (none can solve the problem)
`=1-P(A'nnB')=1-P(A')P(B')`
`=1-(1/2xx2/3)=1-1/3=2/3`
(ii) `P` (exactly one of them solves the problem )
`=P(AnnB')+P(A'nnB)`
`=P(A)P(B')+P(A')P(B)`
`=1/2xx2/3+1/2xx1/3=1/3+1/3=(2+1)/6=3/6=1/2`