Question

A modified roulette wheel has 28 slots. One slot is​ 0, another is​ 00, and the others are numbered 1 through. 26​, respectively. You are placing a bet that the outcome is an even number.​ (In roulette, 0 and 00 are neither odd nor​ even.)

How much profit should you make on the ​$19 bet if you could somehow convince the casino to change its payoff odds so that they are the same as the actual odds against​ winning?

Answer 1

Your expected profit on a $19 bet when betting on an even number in a modified roulette wheel with 28 slots should be $0.

Step-by-step explanation:

To calculate the profit you should make on a $19 bet, we need to determine the odds of winning the bet. In a modified roulette wheel with 28 slots, there are 14 even numbers. Therefore, the probability of the outcome being an even number is 14/28 or 1/2. If the casino changes its payoff odds to match the actual odds against winning, you should expect to win the bet half of the time, and lose the bet half of the time. So, your expected profit on the $19 bet would be the average of winning and losing, which is $0.