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(A) Let $P(A), P(B), P(C)$ be the probabilities that students $A, B, C$ solve the problem respectively.$P(A) = \frac{1}{3}, P(B) = \frac{1}{4}, P(C) =

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$\frac{3}{5}$

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(A) Let $P(A), P(B), P(C)$ be the probabilities that students $A, B, C$ solve the problem respectively.$P(A) = \frac{1}{3}, P(B) = \frac{1}{4}, P(C) = \frac{1}{5}$.The probability that the problem is not solved by any of them is:$P(	ext{not solved}) = (1 - P(A)) 	imes (1 - P(B)) 	imes (1 - P(C))$$P(	ext{not solved}) = (1 - \frac{1}{3}) 	imes (1 - \frac{1}{4}) 	imes (1 - \frac{1}{5})$$P(	ext{not solved}) = \frac{2}{3} 	imes \frac{3}{4} 	imes \frac{4}{5} = \frac{2}{5}$.The probability that the problem is solved is:$P(	ext{solved}) = 1 - P(	ext{not solved}) = 1 - \frac{2}{5} = \frac{3}{5}$.

If three students $A, B, C$ independently solve a problem with probabilities $\frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ respectively,then the probability that the problem will be solved is

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