## 1. From RosenBook

Do Exercises 4.4.20, 5.2.10, 6.4.20, and 6.4.34.

## 2. Not from RosenBook

Homer Simpson obtains a box of n donuts and eats k of them, chosen uniformly at random. Little did he know that r of the donuts were poisoned.

- What is the probability that Homer ate at least one poisoned donut, as a function of n, k, and r?
- The police pick one of the n-k remaining donuts uniformly at random and test it for poison. What is the probability that this donut is poisoned, as a function of n, k, and r?
Suppose that the tested donut

*was*poisoned. What is the probability that Homer ate at least one poisoned donut, conditioned on this fact?