The probabilities of a problem being solved b | vedclass

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Question

(A) Let $A$ be the event that the first student solves the problem,so $P(A) = \frac{1}{2}$.Let $B$ be the event that the second student solves the pro

Vedclass · Accepted Answer

$\frac{2}{3}$

Vedclass · Answer

(A) Let $A$ be the event that the first student solves the problem,so $P(A) = \frac{1}{2}$.Let $B$ be the event that the second student solves the problem,so $P(B) = \frac{1}{3}$.The problem is solved if at least one of the students solves it.The probability that the problem is not solved by either student is $P(A^c) 	imes P(B^c) = (1 - \frac{1}{2}) 	imes (1 - \frac{1}{3}) = \frac{1}{2} 	imes \frac{2}{3} = \frac{1}{3}$.The probability that the problem is solved is $1 - P(	ext{not solved}) = 1 - \frac{1}{3} = \frac{2}{3}$.

The probabilities of a problem being solved by two students are $\frac{1}{2}$ and $\frac{1}{3}$ respectively. What is the probability that the problem is solved?

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