There are two men aged 30 and 36 years. The probability to live 35 years more is 0.67 for 30 -years pld man and 0.60 for 36 year old man. Find the probability that at least one of these men will be alive 35 years hence.  Options
A) 0.35  B) 0.868  C) 0.43  D) 0.44  E) 0.47
Explanation :   Let, A ≡ event that 30 year-old man will live 35 years more.   B ≡ event that 36 year-old man will live 35 years more.   [ A and B are independent events ]   To find at least one of the men will be alive it easier to calculate the complementary of the event (i.e none will be alive) first. Since   P(at least one) = 1 - P(none).   P(none will be alive)   = P(~A~B)   = P(~A) x P(~B)   = [1 - P(A)] x [1 - P(B)]   = (1- 0.67)(1-0.6)   = 0.33 x 0.40   = 0.132   P ( at least one of them will be alive)   = 1 - 0.132   = 0.868.   Answer : 0.868
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There are two men aged 30 and 36 years. The probability to live 35 years more is 0.67 for 30 -years pld man and 0.60 for 36 year old man. Find the probability that at least one of these men will be alive 35 years hence.