Person A can solve 90 % of the problems given | vedclass

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Question

(C) Let $A$ be the event that person $A$ solves the problem and $B$ be the event that person $B$ solves the problem. Given,$P(A) = 0.90$ and $P(B) = 0

Vedclass · Accepted Answer

$0.97$

Vedclass · Answer

(C) Let $A$ be the event that person $A$ solves the problem and $B$ be the event that person $B$ solves the problem. Given,$P(A) = 0.90$ and $P(B) = 0.70$. The probability that person $A$ fails to solve the problem is $P(\bar{A}) = 1 - 0.90 = 0.10$. The probability that person $B$ fails to solve the problem is $P(\bar{B}) = 1 - 0.70 = 0.30$. The probability that at least one of them solves the problem is given by $1 - P(	ext{none solves the problem})$. Since the events are independent,$P(	ext{none solves}) = P(\bar{A}) 	imes P(\bar{B}) = 0.10 	imes 0.30 = 0.03$. Therefore,the probability that at least one of them solves the problem is $1 - 0.03 = 0.97$.

Person $A$ can solve $90 \%$ of the problems given in the book and Person $B$ can solve $70 \%$. Then,the probability that at least one of them will solve the problem selected at random from the book is

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