Q. If the probability that $A$ and $B$ will die with in 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) $p + q - 2pq$
C) $p + q - pq$
D) $p + q + pq$
Explanation
(b)
Given, $P(A) = p,\ \ P(B) = q$
$\Rightarrow P\left( \overline{A} \right) = 1 - P,\ \ P\left( \overline{B} \right) = 1 - q$
Probability that one person is alive there are two cases arise,
(i) $A$ dies and $B$ lives
(ii) $B$ dies and $A$ lives
$\therefore$ Required probability$= p(1 - q) + q(1 - p)$
$= p + q - 2pq$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.