# Given the probability that A can solve a problem is 2/3, and the probability that B can solve the same problem is %, find the probability that

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Given the probability that A can solve a problem is 2/3, and the probability that B can solve the same problem is %, find the probability that

(i) at least one of A and B will solve the problem

(ii) none of the two will solve the problem

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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$\frac{2}{15}$