Question

The probability that the persons $P_1$ and $P_2$ will die in a year are p and q respectively. The probability that at the end of the year only one of them will be alive, is equal to:

• A. p + q - pq
• B. $p+q-p^2-q^2$
• C. p + q - 2pq
• D. pq (p + q - pq)

Answer 1

The correct option is C p + q - 2pq

P (only one of $P_1$ or $P_2$)
$=P\left(P_1\right)+P\left(P_2\right)-2P$ ($P_1$ and $P_2$)
= p + q – 2pq.