Peter and Allen are working on an assignment together. They decide that Peter will work on part (a) only which consists of 5 problems, and Allen will work on part (b) only which consists of 4 other problems. Suppose that Peter can solve a problem by himself before the deadline with a probability of p1, and Allen can solve a problem by himself before the deadline with a probability of p2. (Assume that all questions are equally complicated and that Peter and Allen work independently)
Q: What is the distribution of the number of problems Peter can solve before the deadline, and what is the distribution of the number of problems Allen can solve before the deadline?