Probability Problems Problem:
The probability that a man who is 85 years. old will die before attaining the age of 90 is $\frac13$. A,B,C,D are four person who are 85 years old. what is the probability that A will die before attaining the age of 90 and will be the first to die ?

The probability of dying by 90 is the same for all four.  The probability that A dies first is simply 1/4 since we are give no more information.  Since the two events are independent, the probability of their conjunction, i.e., that A dies and is the first to die, is simply the product of the two probabilities, or 1/12.
