You take a safari trip to the Porobilati game reserve. A highlight of the game reserve is the Poseni river where one can watch deer and elephants coming to drink water. Deer come to the river according to a Poisson process with arrival rate λd=8 per hour; elephants come to the river according to an independent Poisson process with arrival rate λe=2 per hour. On the first day of your safari, you reach the Poseni river early in the morning hoping to see some elephants. Assume that deer and elephants are the only kinds of animals that visit this river.
What's the probability of seeing your 3rd elephant before your 9th deer?
I got this from https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-spring-2006/exams/final.pdf . Any idea of how to solve this problem?