The probability that a 50 year-old man will be alive at 60 is 0.83 and the probability that a 45 year-old woman will be alive at 55 is 0.87. Then

The probability that both will be alive for 10 years, hence i.e., the prob. That the man and his wife Both be alive 10 years hence $0.83\times 0.37=0.7221$.
The prob, that at least one of then will be alive is 1-P(That none of them remains alive 10 years)
$=1-(1-083)(1-0.87)=1-0.17\times 0.13= 0.9779$