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.

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

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