Previous experience with a drug suggests that the probability [math]p[/math] that the drug is effective is a random quantity having a beta density with parameters [math]\alpha = 2[/math] and [math]\beta = 3[/math]. The drug is used on ten subjects and found to be successful in four out of the ten patients. What density should we now assign to the probability [math]p[/math]? What is the probability that the drug will be successful the next time it is used?