You decide to play roulette 4 times, each time betting on red. What is the distribution of X, the number of times you win?

1.

If betting on red, 18/38 = 9/19 chance of winning, so 10/19 chance of losing

Chance of winning 4 times: (9/19) ^4 = 6561/130321 = ~ 5.034%

Chance of winning 3 times: (9/19) ^3 * (10/19) * C (4,1) = 29160/130321 = ~ 22.3755%

Chance of winning 2 times: (9/19) ^2 * (10/19) ^2 * C (4,2) = 48600/130321 = ~ 37.2925%

Chance of winning 1 time: (9/19) * (10/19) ^3 * C (4,3) = 36000/130321 = ~ 27.624%

Chance of winning 0 times: (10/39) ^4 = 10000/130321 = ~ 76.7336%