Question

In American roulette, the wheel has the 38 numbers00, 0, 1, 2, ..., 34, 35, and 36 marked on equally spaced slots. If a player bets $1.00 on a number and wins, then the player keeps the dollar and receives an additional $35.00. Otherwise, the dollar is lost. Find the expected net gain to the player for one play of

Answer 1

Answer:

The expected net gain to the player for one play is -$0.0526.

Step-by-step explanation:

To find the expected net gain, we multiply each outcome by its probability:

Player wins:

Earns $35.

1 out of 38 numbers, so probability 1/38.

Player loses:

Loses $1.

37 out of 38 numbers, so probability 37/38.

Expected value:

$\frac{1}{38} \times 35 - \frac{37}{38} \times 1 = -\frac{2}{38} = -0.0526$

The expected net gain to the player for one play is -$0.0526.