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(B) Let $A$ be the event that $A$ solves the problem and $B$ be the event that $B$ solves the problem.Given $P(A) = \frac{90}{100} = 0.9$ and $P(B) =

Vedclass · Accepted Answer

$\frac{97}{100}$

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(B) Let $A$ be the event that $A$ solves the problem and $B$ be the event that $B$ solves the problem.Given $P(A) = \frac{90}{100} = 0.9$ and $P(B) = \frac{70}{100} = 0.7$.The probability that $A$ does not solve the problem is $P(\bar{A}) = 1 - P(A) = 1 - 0.9 = 0.1$.The probability that $B$ does not solve the problem is $P(\bar{B}) = 1 - P(B) = 1 - 0.7 = 0.3$.The probability that at least one of them solves the problem is $1 - P(	ext{none solves the problem})$.$P(	ext{none solves}) = P(\bar{A}) 	imes P(\bar{B}) = 0.1 	imes 0.3 = 0.03$.Therefore,the required probability is $1 - 0.03 = 0.97 = \frac{97}{100}$.

$A$ can solve $90 \%$ of the problems given in a book and $B$ can solve $70 \%$. What is the probability that at least $1$ of them will solve a problem selected at random from the book?

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