Question

g In American roulette, the wheel has the 38 numbers, 00, 0, 1, 2, ..., 34, 35, and 36, marked on equally spaced slots. If a player bets $1 on a number and wins, then the player keeps the dollar and receives an additional $35. Otherwise, the dollar is lost. Calculate the expected value for the player to play one time. Round to the nearest cent.

Answer 1

Answer:

The expected value for the player to play one time is -$0.05.

Step-by-step explanation:

The expected value of a random variable X is given by the formula:

$E(X)=\sum x\cdot P(X)$

The American roulette wheel has the 38 numbers, {i = 00, 0, 1, 2, ..., 34, 35, and 36}, marked on equally spaced slots.

The probability that the ball stops on any of these 38 numbers is same, i.e.

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

It is provided that a a player bets $1 on a number.

If the player wins, the player keeps the dollar and receives an additional $35.

And if the player losses, the dollar is lost too.

So, the probability distribution is as follows:

    X : $35      -$1

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

Compute the expected value of the game as follows:

$E(X)=\sum x\cdot P(X)$

         $=[\ 35\times \frac{1}{38}]+[-\ 1\times \frac{37}{38}]\\\\=\frac{\ 35-\ 37}{38}\\\\=-\frac{\ 2}{38}\\\\=-\frac{1}{19}\\\\=-0.052632\\\\\approx -\ 0.05$

Thus, the expected value for the player to play one time is -$0.05.