Q: For a certain class of junk bonds, the probability of default in a given year is 0.2. Whether one bond defaults is independent of whether another bond defaults. For a portfolio of five of these junk bonds, what is the probability that zero or one bond of the five defaults in the year ahead?
A: The outcome follows a binomial distribution where n = 5 and p = 0.2. In this case p(0) = 0.85 = 0.3277 and p(1) = 5 × 0.84 × 0.2 = 0.4096, so P(X=0 or X=1) = 0.3277 + 0.4096.
Where does the “5” come from in p(1) = 5 × 0.84 × 0.2 = 0.4096? (or what formula do I use?)
Thank you