Question
Question: The probabilities that A and B will die within a year are p and q respectively, then the probability...
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
Answer
p+q – 2qp
Explanation
Solution
Required probability is P[(A will die and B alive) or (B will die and A alive)]
= P[(A∩B’)U(B∩A’)]
Since events are independent, so
Required probability = P(1). P(B’) + P(2).P(A’)
= p(1 – q) + q(1 – p) = p+q – 2pq.