Question

A Las Vegas roulette wheel has 38 different numerical values. If an individual bets on one number and wins, the payoff is 35 to 1.
a) Show a payoff table for a $10 bet on one number using decision alternatives of bet and do not bet.
b) What is the recommended decision using the expected value approach?

Answer 1

Answer on Question #55602 – Math – Statistics and Probability

A Las Vegas roulette wheel has 38 different numerical values. If an individual bets on one number and wins, the payoff is 35 to 1.

a) Show a payoff table for a $10 bet on one number using decision alternatives of bet and do not bet.

b) What is the recommended decision using the expected value approach?

Solution

a)

b)

$$E[X] = P(Win) \times 340 - P(Lose) \times 10 = \frac{1}{38} \times 340 - \frac{37}{38} \times 10 = -\$0.79 < \$0.$$

The recommended decision using the expected value approach is “do not bet”.

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