Given : Here probability of A and B that can solve the same problem is given , i.e.,
P(A) = \(\frac{2}{3}\) and P(B) = \(\Rightarrow\) P(\(\overline A\)) = P(\(\overline B\)) = \(\frac{2}{5}\)
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\(\frac{13}{15}\)
(ii) none of the two will solve the problem
Now, P(none of the two will solve the problem) = P(\(\overline A\cap \overline B\))
Therefore , none of the two will solve the problem is\(\frac{2}{15}\)