Four persons independently solve a certain pr | vedclass

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(A) Let $P(A) = \frac{1}{2}, P(B) = \frac{3}{4}, P(C) = \frac{1}{4}, P(D) = \frac{1}{8}$ be the probabilities of solving the problem correctly.The pro

Vedclass · Accepted Answer

$\frac{235}{256}$

Vedclass · Answer

(A) Let $P(A) = \frac{1}{2}, P(B) = \frac{3}{4}, P(C) = \frac{1}{4}, P(D) = \frac{1}{8}$ be the probabilities of solving the problem correctly.The probability that the problem is not solved by any of them is $P(\overline{A}) 	imes P(\overline{B}) 	imes P(\overline{C}) 	imes P(\overline{D})$.$P(\overline{A}) = 1 - \frac{1}{2} = \frac{1}{2}$$P(\overline{B}) = 1 - \frac{3}{4} = \frac{1}{4}$$P(\overline{C}) = 1 - \frac{1}{4} = \frac{3}{4}$$P(\overline{D}) = 1 - \frac{1}{8} = \frac{7}{8}$$P(	ext{none solve}) = \frac{1}{2} 	imes \frac{1}{4} 	imes \frac{3}{4} 	imes \frac{7}{8} = \frac{21}{256}$The probability that the problem is solved by at least one person is $1 - P(	ext{none solve}) = 1 - \frac{21}{256} = \frac{235}{256}$.

Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2}, \frac{3}{4}, \frac{1}{4}, \frac{1}{8}$. Then the probability that the problem is solved correctly by at least one of them is

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