The odds against solving a problem by A and B | vedclass

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Question

(A) The odds against $A$ solving the problem are $3:2$,so the probability that $A$ solves it is $P(A) = \frac{2}{3+2} = \frac{2}{5}$. The probability

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$\frac{3}{5}$

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(A) The odds against $A$ solving the problem are $3:2$,so the probability that $A$ solves it is $P(A) = \frac{2}{3+2} = \frac{2}{5}$. The probability that $A$ fails is $P(\bar{A}) = 1 - \frac{2}{5} = \frac{3}{5}$.The odds against $B$ solving the problem are $2:1$,so the probability that $B$ solves it is $P(B) = \frac{1}{2+1} = \frac{1}{3}$. The probability that $B$ fails is $P(\bar{B}) = 1 - \frac{1}{3} = \frac{2}{3}$.The problem is solved if at least one of them solves it. This is the complement of the event that both fail to solve the problem.$P(	ext{solved}) = 1 - P(\bar{A} \cap \bar{B}) = 1 - P(\bar{A}) \cdot P(\bar{B})$$P(	ext{solved}) = 1 - (\frac{3}{5} \cdot \frac{2}{3}) = 1 - \frac{6}{15} = 1 - \frac{2}{5} = \frac{3}{5}$.

The odds against solving a problem by $A$ and $B$ are $3:2$ and $2:1$ respectively. The probability that the problem will be solved is:

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