Question:Fatima and Zack both have labs which end at noon. Every day after the lab they arrive at Satrbucks

located on campus, independently. Zack arrives at time X and Fatima’s arrival time is Y, where X and Y are

measuared in mintues afternoon. The indiviual density functions are:

f1(x) =

e^-x if x is greater or equal to 0,

0 if x < 0

f2(y) =

(1/50)*y if 0 is less than or equal to y less than or equal to 10,

0 if otherwise.

(Zach arrives sometime after noon and is more likely to arrive promptly than late. Fatima always arrives by

12:10 PM and is more likely to arrive late than promptly.) After Fatima arrives, she’ll wait for up to half an hour for

Zack, but he won’t wait for her. Find the probability that they meet.

Thanks!