The probabilities that a man and his wife live for 80 years are \(\frac{2}{3}\) and \(\frac{3}{5}\) respectively. Find the probability that at least one of them will live up to 80 years
A. \(\frac{2}{15}\) B. \(\frac{3}{15}\) C. \(\frac{7}{15}\) D. \(\frac{13}{15}\)
Correct Answer: D
Explanation
Man lives = \(\frac{2}{3}\) not live = \(\frac{1}{3}\) Wife lives = \(\frac{3}{5}\) not live = \(\frac{2}{5}\) P(at least one lives to 80 years) = P(man lives to 80 not woman) + P(woman lives to 80 and not man) + P(both live to 80) \(P = (\frac{2}{3} \times \frac{2}{5}) + (\frac{2}{5} \times \frac{1}{3}) + (\frac{2}{3} \times \frac{3}{5})\) = \(\frac{4}{15} + \frac{3}{15} + \frac{6}{15}\) = \(\frac{13}{15}\)