Question

There are two newborns, Gary and Eric. The future lifetime of Gary is uniformly distributed between 0 to 60 years. The future lifetime of Eric is uniformly distributed between 0 to 40 years. Their future lifetimes are independent. Calculate the probability that Gary dies first

Answer 1

`\text{The probability that Gary dies first = }(1)/(3)`

Explanation:

To find the required probability,

We can split the 40 years of Eric into very small pieces of time dt. Now, If Eric dies at time t and Gary dies before Eric, the probability is :

`(t)/(60)* (dt)/(40)=(t\cdot dt)/(2400)`

Hence the probability that Gary dies first is given by :

`=\int_(0)^(40)(t)/(2400)dt \\\\= (1)/(3)`