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: Option 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})
There is an explanation video available below.