Question

A Nevada roulette wheel had 38 pockets, labeled as 0 00 1 2 3 ... 35 36. One bet is single number. If you bet $1 on a number (any one between 1 and 36) and the number comes up, you get the dollar back together with $35 in winnings; otherwise, you lose your dollar.
A.) Find the probability model of your net gain.

B.) Find the mean of your net gain for one bet.

Answer 1

Answer:

-0.0526

Step-by-step explanation:

Let X be the random variable denoting the net gain(in dollars) for a single trial(one bet).

Assuming that each number in the wheel is equally likely, probability of the outcome being a victory is $\frac{1}{38}$ and probability of failure is $\frac{37}{38}$. For a win, X takes value 35 and for a loss X takes value -1. So the model is,

$P(X=35) = \frac{1}{38}$

$P(X=-1) = \frac{37}{38}$

$P(X=i) = 0 \;if\; i \neq 38, i\neq -1$

The mean for one bet is $E(X) = \sum xP(X=x) = 35\times\frac{1}{38} - 1\times\frac{37}{38} = -0.0526$