Question

In the casino game of roulette, a $1 bet on red pays $2 with probability 18/38 and $0 with probability 20/38. So if X denotes the net winnings on a single bet, the distribution of X is given by the________.

Answer 1

`P_X(1) = 9/19`

`P_X(-1) = 10/19`

Explanation:

You need to take the payment and substract $1 from them, corresponding to the bet cost. With this in mind, you will win $1 with probability 18/38 = 9/19 and you will lose $1 with probability 20/38 = 10/19. With this in mind, the distribution of X is given by the following probability mass function, with range {-1,1}

`P_X(1) = 9/19`

`P_X(-1) = 10/19`