**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\(\frac{2}{15}\)