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(A) Let $P(A) = \frac{1}{2}$,$P(B) = \frac{1}{4}$,and $P(C) = \frac{1}{6}$ be the probabilities of the three students solving the question.The questio

Vedclass · Accepted Answer

$\frac{33}{48}$

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(A) Let $P(A) = \frac{1}{2}$,$P(B) = \frac{1}{4}$,and $P(C) = \frac{1}{6}$ be the probabilities of the three students solving the question.The question is solved if at least one of them solves it. The probability that the question is solved is $P(A \cup B \cup C) = 1 - P(	ext{none of them solve it})$.The probability that student $A$ does not solve it is $P(\bar{A}) = 1 - \frac{1}{2} = \frac{1}{2}$.The probability that student $B$ does not solve it is $P(\bar{B}) = 1 - \frac{1}{4} = \frac{3}{4}$.The probability that student $C$ does not solve it is $P(\bar{C}) = 1 - \frac{1}{6} = \frac{5}{6}$.Since the events are independent,the probability that none of them solve it is $P(\bar{A}) 	imes P(\bar{B}) 	imes P(\bar{C}) = \frac{1}{2} 	imes \frac{3}{4} 	imes \frac{5}{6} = \frac{15}{48}$.Therefore,the probability that the question is solved is $1 - \frac{15}{48} = \frac{48 - 15}{48} = \frac{33}{48}$.

The probabilities of three students solving a question are $\frac{1}{2}, \frac{1}{4},$ and $\frac{1}{6}$ respectively. What is the probability that the question is solved?

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