Question

A roulette wheel consists of 18 black slots, 18 red slots, and 2 green slots. If a gambler bets $10 on red, what is the gamblers expected gain or loss?

Answer 1

Let the winning amount be w.

There are 18 red slots out of 18 + 18 + 2 = 38.

Probability that the bet on red is a success $= \frac{18}{38}$

Probability that the bet on red is not a success $= 1 - \frac{18}{38} = \frac{20}{38}$

=> Expected value $= w \times \frac{18}{38} - \$10 \times \frac{20}{38}$

If w = $10 for instance, expected loss $= \$10 \times \frac{18}{38} - \$10 \times \frac{20}{38}$

= -0.5263$.