The probabilities of solving a specific probl | vedclass

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(C) Let $P(A)$ be the probability that $A$ solves the problem,$P(A) = \frac{1}{2}$.Let $P(B)$ be the probability that $B$ solves the problem,$P(B) = \

Vedclass · Accepted Answer

$\frac{2}{3}$

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(C) Let $P(A)$ be the probability that $A$ solves the problem,$P(A) = \frac{1}{2}$.Let $P(B)$ be the probability that $B$ solves the problem,$P(B) = \frac{1}{3}$.The problem is solved if at least one of them solves it.The probability that the problem is not solved by either is $P(A') 	imes P(B')$.$P(A') = 1 - P(A) = 1 - \frac{1}{2} = \frac{1}{2}$.$P(B') = 1 - P(B) = 1 - \frac{1}{3} = \frac{2}{3}$.Probability that the problem is not solved $= P(A') 	imes P(B') = \frac{1}{2} 	imes \frac{2}{3} = \frac{1}{3}$.Probability that the problem is solved $= 1 - P(	ext{not solved}) = 1 - \frac{1}{3} = \frac{2}{3}$.

The probabilities of solving a specific problem independently by $A$ and $B$ are $\frac{1}{2}$ and $\frac{1}{3}$ respectively. If both try to solve the problem independently,find the probability that the problem is solved.

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