Question

1. An American roulette wheel contains 38 numbers: 18 are red, 18 are black, and 2 are green. When the roulette wheel is spun, the ball is equally likely to land on any of the 38 numbers. Suppose that you bet $1 on red. If the ball lands on a red number, you win $1; otherwise you lose your $1. Let X be the amount you win on your $1 bet.

1. Determine the probability distribution of the random variable X .

Answer 1

Since, the ball is equally likely to land on any of the numbers thus, probability that:

It lands on red is :18/38

It lands on black is: 18/38

It lands on green is: 2/38

Now I win only if the ball lands on red. Thus, probability I win is: 18/38

Hence, probability I don't win is: 1-18/38=20/38

Thus, X takes $1, if I win else it takes -$1 if I loose (winning a negative value is losing the absolute amount)

Thus, X takes 1 w.p. 18/38=9/19 and takes -1 w.p. 20/38=10/19

This is the required distribution of X