At the time of a certain marriage, the probabilities that the man and the woman will both live fifty more years are 0.352 and 0.500, respectively. what is the probability that both will be alive fifty years later?

If I understood correctly, the possibility of the man living 50 more years is 0.352, and the possibility of the woman living 50 more years is 0.5

We have to multiply both possibilities to get their union set, in this case, both being alive. In other words, we are going to consider the times both of these events are happening.

0.352 x 0.5 = 0.176