The probability that a man will be alive in 25 years is 3/5, and that the wife will be alive in 25 years is 2/3. What's the probability that in 25 years, both will be alive?

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Answer 1 · 2017-01-23T16:06:23

$The Reqd. Prob.= \frac{2}{5} = 0.4$ $"The Reqd. Prob.="2/5=0.4$

Let, $M =$ $M=$ the Event that a Man will be alive in $25$ $25$ years, and,

$W =$ $W=$ the Event that the (Man's) Wife (!) will be alive in $25$ $25$ years.

We are said that, $P (M) = \frac{3}{5}, and, P (W) = \frac{2}{3}$ $P(M)=3/5, and, P(W)=2/3$ .

We require $P (M \cap W)$ $P(MnnW)$

Observe that, $M and W$ $M and W$ are Independent Events , so that,

$P (M \cap W) = P (M) P (W)$ $P(MnnW)=P(M)P(W)$ . Hence,

$The Reqd. Prob.= (\frac{3}{5}) (\frac{2}{3}) = \frac{2}{5} = 0.4$ $"The Reqd. Prob.="(3/5)(2/3)=2/5=0.4$

Enjoy Maths.!