The probability that a man will be alive 25 y | vedclass

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Question

(C) Let $A$ be the event that the man is alive after $25$ years and $B$ be the event that the wife is alive after $25$ years.Given: $P(A) = 0.3$ and $

Vedclass · Accepted Answer

$0.28$

Vedclass · Answer

(C) Let $A$ be the event that the man is alive after $25$ years and $B$ be the event that the wife is alive after $25$ years.Given: $P(A) = 0.3$ and $P(B) = 0.4$.The probability that the man is not alive is $P(A') = 1 - P(A) = 1 - 0.3 = 0.7$.We need to find the probability that only the woman will be alive,which means the woman is alive $(B)$ and the man is not alive $(A')$.Since these are independent events,the required probability is $P(A' \cap B) = P(A') 	imes P(B)$.Required probability $= 0.7 	imes 0.4 = 0.28$.

The probability that a man will be alive $25$ years hence is $0.3$,and the probability that his wife will be alive $25$ years hence is $0.4$. Find the probability that $25$ years hence,only the woman will be alive.

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