1. A fair die is rolled 12 times. Given that there are exactly two ones, what is the probability that there are exactly two sixes?

2. A fair die is rolled twice. Compute the probability that the sum of the two rolls is 3, 5, 7, 9, 11, respectively, given that the sum is odd.

3. A fair die was rolled four times. The faces 1 and 2 never appeared. What is the probability that the other four faces each appeared exactly once?

4. Jeff, Jen, and Cathy shoot at a bull's eye. They can hit the bull's eye 70%; 80%, and 75% of the time, respectively. One of the three is known to have hit the bull's eye. Find the probability that it was Jen.

5. A fair coin is tossed ten times. Given that at least seven heads were obtained, what is the probability that the first toss was a head? That at least one of the first two tosses was a head? That the first two tosses were both heads?