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

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

a) on any individual roll what is the probability that the player rolls (1,1)

b) 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?

c) 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 is successful)?

Solution

a) Total possible cases=36

on any individual roll what is the probability that the player rolls (1,1) is 1/36

b) 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),. here we use Binomail distribution

c) average is np