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?
To win on a scratch card you have to uncover three numbers that add
up to more than fifteen. What is the probability of winning a
Which of these games would you play to give yourself the best possible chance of winning a prize?
In how many ways can the number 1 000 000 be expressed as the
product of three positive integers?