1. (Excel spreadsheet)

2. (Maple worksheet)

3. 1. The test is a fair bet for someone who has a 50% chance of passing (because there is a 50% chance of winning $50,000, and a 50% chance of losing $50,000).
      So the probability of passing the test (for those who take it) is between 50% and 100%, uniformly distributed, and the average person taking the test then has a 75% chance of passing.
   2. The test is now a fair bet for a woman who has a 10% chance of passing (because there is a 10% chance of winning $90,000, and a 90% chance of losing $10,000).
      So the probability of passing the test (for women who take it) is between 10% and 100%, uniformly distributed, and the average person taking the test then has a 55% chance of passing.