Probabilities that A and B will die within a year are p and q respectively, then probability that on

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14.Probability

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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

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