A new therapy is being developed by a business. In two out of three pilot instances, the therapy was shown to be effective. The corporation wants to know how successful the next experiment, which will involve four people, will be. The company has decided to use a prior for their trial for the success rate, p, as a Beta(p|3,2) distribution. Describe how this prior relates to the material that has been made available thus far. Calculate the probability that the therapy will work for at least three of the four persons evaluated in the second trial after it is completed by determining the posterior predictive distribution expression.