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:
[tex]E(X)=\sum x\cdot P(X)[/tex]
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) = [tex]\frac{1}{38}[/tex].
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) : [tex]\frac{1}{38}[/tex] [tex]\frac{37}{38}[/tex]
Compute the expected value of the game as follows:
[tex]E(X)=\sum x\cdot P(X)[/tex]
[tex]=[\$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[/tex]
Thus, the expected value for the player to play one time is -$0.05.
