From Bayesian statistics, the posterior distribution of parameter p of a binomial distribution has a beta distribution if the prior distribution of p is uniform. The parameters is given by the number of events that happen with probability p while is given by the number of events that happen with probability 1-p.

For this question, let H denote the event that in a sample of one hundred MP3 players, 1 is found to be defective. Then,

Using Bayes' theorem and total probability, we have

which is a beta distribution with parameters 2 and 100(and 1 and 0 for the finite support).