Need help with some Probability questions

6. You flip a coin three times. What is the probability of all heads given the last coin is heads? 7. If you roll three dice, what is the probability of the same number appearing on more than one die? (Hint: It is easier to count the number of outcomes in which every die shows a different number than it is to count the number of outcomes in which at least two dice show the same number.) 8. In class we looked at the problem of using Bayes' Law to compute the probability of whether a biased or fair coin was used in making some coin flips. Do the calculations yourself, but this time assume the flips resulted in 2 heads and 1 tails. Do not assume the coin flips happened in the order of H, H, T -- only that a total of 2 heads was obtained. What is the probability you flipped the biased coin