Given : Here probability of A and B that can solve the same problem is given , i.e.,
P(A) =
2
3
and P(B) = ⇒
P(
¯
A
) = P(
¯
B
) =
2
5
Also, A and B are independent . not A and not B are independent.
To Find:
(i) atleast one of A and B will solve the problem
Now , P(atleast one of them will solve the problem) = 1 – P(both are unable to solve)
Therefore , atleast one of A and B will solve the problem is
13
15
(ii) none of the two will solve the problem
Now, P(none of the two will solve the problem) = P(
¯
A
∩
¯
B
)
Therefore , none of the two will solve the problem is
2
15
