Can someone help me with this problem:
A certain police officer stops cars for speeding. The number of red sports cars she stops in one hour is a Poisson process with rate 4, while the number of other cars she stops is a Poisson process with rate 1. Assume that these two processes are independent of each other. Find the probability that this police officer stops at least 2 ordinary cars before she stops 3 red sports cars.
Are you supposed to view this as a merged process and count the amount of time it takes until the 3rd arrival of the red sports car? But I'm not sure how to address the "at least 2 ordinary cars" part of the question. Any help would be appreciated, thanks!