1. Anne and Billy are playing a simple dice game. Each rolls one die and the one with higher number wins if the higher number is at least two more than the lower number. If the numbers are the same, or if the numbers differ by only one, they roll again. If Anne just won, what is the probability that she rolled a '5'? 2. In a widget factory, machines A, B, and C manufacture, respectively, 20, 30, and 50 percent of the total. Of their output 6, 3, and 2 percent are defective widgets. A widget is drawn at random from the produce and is found defective. What are the probabilities that it was manufactured by machines A, B, and C? 3. Students in public schools in Texas take a standardized test called the Texas Assessment of Academic Skills Test (TAAS). For children in grade 5, the TAAS consists of two tests, one in reading and one in math. In 1994, across the state 77.9% of fifth graders passed the reading test, 63.0% passed the math test, and 58.6% passed both. What is the probability that a random fifth grader passed the reading test or the math test?