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14.Probability
medium
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
A
$p + q$
B
$p + q - 2qp$
C
$p + q - pq$
D
$p + q + pq$
Solution
(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.$
Standard 11
Mathematics