Consider a classroom of 21 kids. 20 of the kids are healthy (and susceptible to getting sick) on Day 1. John (the

21st kid) walks in sick and starts interacting with the other kids. Let's suppose that John comes to school every day (whether

or not he's sick) and will be infectious for 3 days. Thus, there are 3 chances for John to infect the other kids - Days 1, 2, and 3. Suppose that the probability hat he infects any individual susceptible kid on any of the three days is p = 0:02; and suppose that all kids and days are independent (so that you have i.i.d. Bern(p) trials). If a kid gets infected by John, he will then become infectious for 3 days as well, starting on the next day.

What is the distribution of the number of kids that John infects on Day 1?

What is the expected number of kids that John infects on Day 1?