The probabilities of a husband and his wife surviving for 20 more years are 0 8 and 0 9 respectively - Maths - Probability

Question

The probabilities of a husband and his wife surviving for
20 more years are 0 8 and 0 9 respectively Find the probability
that after 20 years: a both of them are alive b at least one of
them is alive

Manbar Singh · Accepted Answer

Let A be the event that a husband will be alive after 20 yrs
Let B be the event that a wife will be alive after 20 yrs
Now, PA = 0 8; PB = 0
9Now, PA = 1-PA = 1 - 0
8 = 0
2Now, PB 1 - PB = 1 - 0
9 = 0 1a
Probability that both of them are alive = PA 
 PB = 0 8×0 9 = 0 72b
Probability that none of them is alive = PA 
 PB = 0 2×0 1 = 0
02Probability that at least one of them is alive = 1 - 0
02 = 0 08

The probabilities of a husband and his wife surviving for 20 more years are 0.8 and 0.9 respectively. Find the probability that after 20 years: a. both of them are alive b. at least one of them is alive.