The probabilities that A and B will die withi | vedclass

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Question

(b) Required probability is

$P$[($A$ will die and $B$ alive) or ($B$ will die and $A$ alive)]

$ = P[(A \cap B') \cup (B \cap A')]$

Si

Vedclass · Accepted Answer

$p + q - 2qp$

Vedclass · Answer

(b) Required probability is

$P$[($A$ will die and $B$ alive) or ($B$ will die and $A$ alive)]

$ = P[(A \cap B') \cup (B \cap A')]$

Since events are independent, so

Required probability$ = P(A)\,.\,P(B') + P(B)\,.\,P(A')$

$ = p\,.\,(1 - q) + q(1 - p) = p + q - 2pq.$

The probabilities that $A$ and $B$ will die within a year are $p$ and $q$ respectively, then the probability that only one of them will be alive at the end of the year is

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