The answers in this problem have to be actual numbers. And you have to show clearly how you derive/prove your answers. Buses A and B arrive at a bus stop as mutually independent Poisson processes with rates 2 buses/hour and 3 buses/hour, respectively. Alice and Bob arrive at the bus stop simultaneously at 4pm; Alice needs to take bus A, and Bob needs to take bus B. 1.1. (10 points) What is the probability that both Alice and Bob will take a bus before 4:20pm? 1.2. (15 points) What is the probability that Alice and Bob will take their buses within 20 min of each other