Three students A, B,and C are given a mathema | vedclass

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(C) Let $P(A), P(B)$,and $P(C)$ be the probabilities of students $A, B$,and $C$ solving the problem respectively.$P(A) = 1/2, P(B) = 1/3, P(C) = 1/4$.

Vedclass · Accepted Answer

$3/4$

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(C) Let $P(A), P(B)$,and $P(C)$ be the probabilities of students $A, B$,and $C$ solving the problem respectively.$P(A) = 1/2, P(B) = 1/3, P(C) = 1/4$.The probability that the problem is not solved by $A, B$,and $C$ is given by $P(A'), P(B')$,and $P(C')$ respectively.$P(A') = 1 - 1/2 = 1/2$.$P(B') = 1 - 1/3 = 2/3$.$P(C') = 1 - 1/4 = 3/4$.The probability that the problem is not solved by any of them is $P(	ext{none}) = P(A') 	imes P(B') 	imes P(C') = (1/2) 	imes (2/3) 	imes (3/4) = 1/4$.The probability that the problem is solved is $P(	ext{solved}) = 1 - P(	ext{none}) = 1 - 1/4 = 3/4$.

Three students $A, B$,and $C$ are given a mathematics problem. The probabilities of them solving the problem are $1/2, 1/3$,and $1/4$ respectively. What is the probability that the problem is solved?

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