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Question

(A) Let $A$,$B$,and $C$ be the events that the three persons solve the problem independently.Given probabilities are $P(A) = \frac{1}{3}$,$P(B) = \fra

Vedclass · Accepted Answer

$\frac{2}{5}$

Vedclass · Answer

(A) Let $A$,$B$,and $C$ be the events that the three persons solve the problem independently.Given probabilities are $P(A) = \frac{1}{3}$,$P(B) = \frac{1}{4}$,and $P(C) = \frac{1}{5}$.The probability that they do not solve the problem is given by $P(A') = 1 - P(A) = 1 - \frac{1}{3} = \frac{2}{3}$,$P(B') = 1 - P(B) = 1 - \frac{1}{4} = \frac{3}{4}$,and $P(C') = 1 - P(C) = 1 - \frac{1}{5} = \frac{4}{5}$.Since the events are independent,the probability that none of them solve the problem is $P(A' \cap B' \cap C') = P(A') 	imes P(B') 	imes P(C')$.$P(A' \cap B' \cap C') = \frac{2}{3} 	imes \frac{3}{4} 	imes \frac{4}{5} = \frac{2}{5}$.

Three persons work independently on a problem. If the respective probabilities that they will solve it are $\frac{1}{3}$,$\frac{1}{4}$,and $\frac{1}{5}$,then the probability that none can solve it is:

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