A mathematics problem is given to three stude | vedclass

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Question

(A) 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

$3/4$

Vedclass · Answer

(A) 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 any of them is the probability that all three fail to solve it.$P(	ext{not } A) = 1 - 1/2 = 1/2$.$P(	ext{not } B) = 1 - 1/3 = 2/3$.$P(	ext{not } C) = 1 - 1/4 = 3/4$.Since the events are independent,the probability that none of them solve the problem is:$P(	ext{none}) = P(	ext{not } A) 	imes P(	ext{not } B) 	imes P(	ext{not } C) = (1/2) 	imes (2/3) 	imes (3/4) = 1/4$.The probability that the problem is solved is $1 - P(	ext{none})$.$P(	ext{solved}) = 1 - 1/4 = 3/4$.

$A$ mathematics problem is given to three students $A, B$,and $C$. 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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