We are going to observe the number of "successes" in n = 100 independent trials. We have prior experience and believe that a beta(6,14) summarizes our prior experience. However, we consider that our prior experience may have occurred under different conditions, so our prior may be bad. We decide to use a mixture prior where g₀(π) is the beta(6, 14) and g₁(π) is the beta(1, 1) distribution, and the prior probability P(I = 0) = .95. Suppose we take a random sample of n = 100 and observe y = 36 successes.