A problem in Algebra is given to two students | vedclass

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Question

(A) Let $P(A)$ be the probability that student $A$ solves the problem,so $P(A) = \frac{2}{5}$.Let $P(B)$ be the probability that student $B$ solves th

Vedclass · Accepted Answer

$\frac{17}{20}$

Vedclass · Answer

(A) Let $P(A)$ be the probability that student $A$ solves the problem,so $P(A) = \frac{2}{5}$.Let $P(B)$ be the probability that student $B$ solves the problem,so $P(B) = \frac{3}{4}$.The probability that student $A$ does not solve the problem is $P(A') = 1 - P(A) = 1 - \frac{2}{5} = \frac{3}{5}$.The probability that student $B$ does not solve the problem is $P(B') = 1 - P(B) = 1 - \frac{3}{4} = \frac{1}{4}$.The problem is solved if at least one of them solves it. This is the complement of the event that neither of them solves the problem.Probability that neither solves the problem = $P(A') 	imes P(B') = \frac{3}{5} 	imes \frac{1}{4} = \frac{3}{20}$.Probability that the problem is solved = $1 - P(	ext{neither solves}) = 1 - \frac{3}{20} = \frac{17}{20}$.

$A$ problem in Algebra is given to two students $A$ and $B$ whose chances of solving it are $\frac{2}{5}$ and $\frac{3}{4}$ respectively. The probability that the problem is solved if both of them try independently is

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