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, 

(i) both of them are alive 

(ii) atleast one of them is alive

Answer 1

Let P(H) = 0.8 , P(W) = 0.9

(i) P(both alive) = P(H ∩ W) = P(H). P(W)

Since Husband and wife are independent.

P(H ∩ W) = 0.8 × 0.9 = 0.72

(ii) P(atleast one of them is alive)

= P(H ∪ W) = P(H) + P(W) – P(H ∩ W) 

= 0.8 + 0.9 – 0.72 

= 0.98.