Mathematics 2012 JAMB Past Questions - Question 50: The probability that a man and his wife lives for 80 years are 2/3 and 3/5 respectively .find the probability that at least one of them will live up to 80years.

Correct Answer

D

Explanation

Man lives = 2/3 not = 1/3wife lives = 3/5 not = 2/5P (2/3 X 2/5) + (2/3 X 3/5) = 4/15 + 3/15 +6/15 = 13/15To find the probability that at least one of them will live up to 80 years, we can use the concept of complementary probability.Let's denote the probability that the man lives up to 80 years as P(M) = 2/3, and the probability that his wife lives up to 80 years as P(W) = 3/5.The probability that both the man and his wife do not live up to 80 years is the complement of at least one of them living up to 80 years.The probability that the man does not live up to 80 years is 1 - P(M) = 1 - 2/3 = 1/3.The probability that the wife does not live up to 80 years is 1 - P(W) = 1 - 3/5 = 2/5.To find the probability that both the man and his wife do not live up to 80 years, we multiply their individual probabilities:P(both not living up to 80 years) = (1/3) * (2/5) = 2/15.The probability that at least one of them will live up to 80 years is the complement of both not living up to 80 years:P(at least one living up to 80 years) = 1 - P(both not living up to 80 years) = 1 - 2/15 = 13/15.Therefore, the probability that at least one of them will live up to 80 years is 13/15.