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?
A gambler bets half the money in his pocket on the toss of a coin,
winning an equal amount for a head and losing his money if the
result is a tail. After 2n plays he has won exactly n times. Has he
more money than he started with?
A counter is placed in the bottom right hand corner of a grid. You
toss a coin and move the star according to the following rules: ...
What is the probability that you end up in the top left-hand corner
of the grid?
Click below for an algebraic approach using tree diagrams.