The probability that a man and his wife will | vedclass

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Question

(D) Let $P(M)$ be the probability that the man is alive and $P(W)$ be the probability that the wife is alive.Given $P(M) = \frac{1}{4}$ and $P(W) = \f

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

(D) Let $P(M)$ be the probability that the man is alive and $P(W)$ be the probability that the wife is alive.Given $P(M) = \frac{1}{4}$ and $P(W) = \frac{1}{3}$.The probability that the man is not alive is $P(M') = 1 - P(M) = 1 - \frac{1}{4} = \frac{3}{4}$.The probability that the wife is not alive is $P(W') = 1 - P(W) = 1 - \frac{1}{3} = \frac{2}{3}$.Since the events are independent, the probability that neither is alive is $P(M' \cap W') = P(M') 	imes P(W')$.$P(M' \cap W') = \frac{3}{4} 	imes \frac{2}{3} = \frac{6}{12} = \frac{1}{2}$.

Outcome	Probability
$\omega_{1}$	$\frac{1}{14}$
$\omega_{2}$	$\frac{2}{14}$
$\omega_{3}$	$\frac{3}{14}$
$\omega_{4}$	$\frac{4}{14}$
$\omega_{5}$	$\frac{5}{14}$
$\omega_{6}$	$\frac{6}{14}$
$\omega_{7}$	$\frac{15}{14}$

The probability that a man and his wife will be alive after $20 \text{ years}$ are $\frac{1}{4}$ and $\frac{1}{3}$ respectively. The probability that neither the man nor his wife will be alive after $20 \text{ years}$ is

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