1. Each of three sealed opaque envelopes contains two bills. One envelope contains two $1 bills, another contains two $5 bills, and the third contains a $1 bill and a $5 bill. An envelope is selected at random, and a bill is taken from the envelope at random. If it is a $5 bill, what is the probability that the other bill in the envelope is also a $5 bill?
2. Consider three boxes. One box contains two gold coins, one box contains two silver coins, and one box contains a gold coin and a silver coin. Suppose that you select a box at random and then select a coin at random from that box. If the coin is gold, what is the probability that the other coin in the box is gold?
3. A sequence of two playing cards is drawn at random (without replacement) from a standard deck of 52 cards. What is the probability that both cards are kings?
4. A sequence of two playing cards is drawn at random (without replacement) from a standard deck of 52 cards. What is the probability that both cards are diamonds?