Conditional probability

What percentage of students who graduate have never been to France?

How can we find out answers to questions like this if people often lie?

How do different drug-testing regimes affect the risks and payoffs for an athlete who chooses to take drugs?

If the score is 8-8 do I have more chance of winning if the winner is the first to reach 9 points or the first to reach 10 points?

A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

Use cunning to work out a strategy to win this game.

You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by a head (you win). What is the probability that you win?

You have two bags, four red balls and four white balls. You must put all the balls in the bags although you are allowed to have one bag empty. How should you distribute the balls between the two bags so as to make the probability of choosing a red ball as small as possible and what will the probability be in that case?

In how many different ways can I colour the five edges of a pentagon so that no two adjacent edges are the same colour?

Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions?