Q. 14

# 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

Answer :

Given : Here probability of A and B that can solve the same problem is given , i.e., P(A) = and P(B) = P() = and P() =

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)

= 1 - P()

= 1- P() P()

= 1-

=

Therefore , atleast one of A and B will solve the problem is

ii) none of the two will solve the problem

Now, P(none of the two will solve the problem) = P()

= P() P()

=

=

Therefore , none of the two will solve the problem is

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