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

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