In a board game a player can get out of jail by rolling the

In a board game, a player can get out of jail by rolling the pair (1,1) with 2 ordinary 6 sided dice.

1. On any individual roll what is the probability that the player rolls (1,1)?

2. If X is the random variable that models the number of rolls a player takes to achieve the outcome (1,1) (including the roll on which the player is successful), what is the distribution of X?

3. On average, how many consecutive rolls can a player expect that it will take in order to achieve the desired outcome of (1,1) (including the roll on which the player was successful)?

Solution