A problem in Algebra is given to two students | vedclass

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(A) Let $P(A)$ be the probability that student $A$ solves the problem and $P(B)$ be the probability that student $B$ solves the problem. Given $P(A) =

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$\frac{17}{20}$

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(A) Let $P(A)$ be the probability that student $A$ solves the problem and $P(B)$ be the probability that student $B$ solves the problem. Given $P(A) = \frac{2}{5}$ and $P(B) = \frac{3}{4}$. The problem is solved if at least one of them solves it. $P(	ext{problem is solved}) = 1 - P(	ext{problem is not solved})$. Since $A$ and $B$ try independently, the probability that neither solves it is $P(\bar{A}) 	imes P(\bar{B})$. $P(\bar{A}) = 1 - P(A) = 1 - \frac{2}{5} = \frac{3}{5}$. $P(\bar{B}) = 1 - P(B) = 1 - \frac{3}{4} = \frac{1}{4}$. $P(	ext{problem is solved}) = 1 - (\frac{3}{5} 	imes \frac{1}{4}) = 1 - \frac{3}{20} = \frac{17}{20}$.

$A$ 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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