In a clinical trial, let the probability of successful outcome have a prior distribution that is

In a clinical trial, let the probability of successful outcome θ have a prior distribution that is the uniform distribution on the interval [0, 1], which is also the beta distribution with parameters 1 and 1. Suppose that the first patient has a successful outcome. Find the Bayes estimates of θ that would be obtained for both the squared error and absolute error loss functions.