A major credit rating agency rates a bond of a company as CCC if the probability of default

is 0.10 in any given year and defaults across years are independent.

a) What is the probability that a CCC bond defaults in the 4th year (that is, the company

goes for 3 years without default, then defaults in the fourth)?

b) Suppose you own a pool of 20 CCC bonds from 20 different companies. Assume the

default risks for different companies are independent. What is the probability that

between 1 and 3 of these CCC bonds (that is either one or two or three CCC bonds)

default in the first year?