It is 5:2 against a husband who is 65 years o | vedclass

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(C) Let $H$ be the event that the husband lives for $20$ years and $W$ be the event that the wife lives for $20$ years.Given the odds against the husb

Vedclass · Accepted Answer

$29$

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(C) Let $H$ be the event that the husband lives for $20$ years and $W$ be the event that the wife lives for $20$ years.Given the odds against the husband living for $20$ years are $5:2$,the probability that he does not live is $P(\overline{H}) = \frac{5}{5+2} = \frac{5}{7}$.Thus,the probability that he lives is $P(H) = 1 - \frac{5}{7} = \frac{2}{7}$.Given the odds against the wife living for $20$ years are $4:3$,the probability that she does not live is $P(\overline{W}) = \frac{4}{4+3} = \frac{4}{7}$.Thus,the probability that she lives is $P(W) = 1 - \frac{4}{7} = \frac{3}{7}$.The probability that at least one of them will be alive is $k = 1 - P(\overline{H} \cap \overline{W})$.Since the events are independent,$k = 1 - P(\overline{H}) 	imes P(\overline{W})$.$k = 1 - (\frac{5}{7} 	imes \frac{4}{7}) = 1 - \frac{20}{49} = \frac{29}{49}$.Therefore,$49k = 49 	imes \frac{29}{49} = 29$.

It is $5:2$ against a husband who is $65$ years old living till he is $85$ and $4:3$ against his wife who is now $58$,living till she is $78$. If the probability that at least one of them will be alive for $20$ years is $k$,then the value of $49k$ is:

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