1. There is a deck of 3 cards, ace of hearts (AH), ace of diamonds (AD) and jack of hearts (JH). You draw two cards simultaneously. One is AD. What's the probability that the other card you drew is an ace? [Answer: 1/2]. Hint: remember that drawing two cards together is the same as drawing one after the other without replacement.

2.One of 3 slot machines pays off with probability 1/2, while each of the other two pays off with probability 1/3. You do not know which is which. You play twice on a randomly selected machine, losing the first time and winning the second. What's the probability that you have played the favorable machine? [Answer: 9/25]

3.Three machines, A, B, and C produce 50%, 30% and 20% of the items of a factory. The percentage of defective output for these machines is 3% for A, 4% for B, and 5% for C. Given that an item randomly selected is defective, what's the probability it came from A? [Answer: 15/37. Sorry about the ugly numbers here!]

4. In democracyville, 30% of eligible voters are conservatives, 50% liberals, and 20% independents. 90% of conservatives, 80% of liberals, and 50% of independents vote. Voting has taken place. If a randomly picked eligible voter has not voted, what's the probability she's a liberal? [Answer: 10/23]