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

Answer:

$\text{The probability that Gary dies first = }\frac{1}{3}$

Step-by-step 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 :

$\frac{t}{60}\times \frac{dt}{40}=\frac{t\cdot dt}{2400}$

Hence the probability that Gary dies first is  given by :

$=\int_{0}^{40}\frac{t}{2400}dt \\\\= \frac{1}{3}$