1. Josh takes a twenty-question multiple-choice exam where each question has five answers. Some of the answers he kn ows, while others he gets right just by making lucky guesses. Suppose that the conditional probability of his knowing the answer to a randomly selected q uestion given that he got it right is 0.92. How many of the Lwenty queslions was he prepared for?

2. Recen tly the U.S. Senate Committee on Labor and Public Welfare investigated t he (easlbility of setting up a national screening progra m to detect child abuse. A team of consultan ts estimated the following probabiHlies: (1) one child in ninety is abused, (2) a physician can detect an abused child 90% of the time, and (3) a screening program would incorrectly l abel 3% of alJ non abused children as abused. What is the probability that a child is actually abused given that the screening program makes that diagnosis? How does the probabili ty change if the incidence of abuse is one in one Lhousand? Or one in fifty?