The probability that a 50-year old man will be alive till age 60 is 0.83 and the probability that a 45-year old woman will be alive till age 55 is 0.97. What is the probability that a man whose age is 50 and his wife whose age is 45 will both be alive after 10 years?
Let A be the event that man will be alive at 60.
∴ P(A) = 0.83
Let B be the event that woman will be alive at 55.
∴ P(B) = 0.97
A ∩ B = Event that both will be alive.
Also, A and B are independent events
∴ P(both man and his wife will be alive)
= P(A ∩ B)
= P(A) · P(B)
= 0.83 × 0.97