1. Consider two urns. The ?rst contains two white and seven black balls, and the second contains ?ve white and six black balls. We ?ip a fair coin and then draw a ball from the ?rst urn or the second urn depending on whether the outcome was heads or tails. What is the conditional probability that the outcome of the toss was heads given that a white ball was selected?

2. In answering a question on  a  multiple-choice  test  a  student either knows the answer or guesses. Let p be the probability that she knows the answer and 1 - p the probability that she guesses. Assume that a student who guesses at the answer will be correct with probability 1/m, where m is the number of multiple-choice alternatives. What is the conditional probabil- ity that a student knew the answer to a question given that she answered it correctly?