Question 3.2: A roulette wheel consists of 18 black slots, 18 red slots, a......
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 gambler’s expected gain or loss?
Define the r.v. X by: X = 10 with probability 18/38 and X = −10 with probability 20/38, or in a tabular form
Then E X=10\times{\frac{18}{38}}-10\times{\frac{20}{38}}=-{\frac{10}{19}}\simeq-0.526. Thus, the gambler’s expected loss is about 53 cents.
| x | 10 | -10 | Total |
| f(x) | \frac{18}{38} | {\frac{20}{38}} | 1 |
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