One option in a roulette game is to bet $8 on red. There are 18 red compartments, 18 black compartments, and two compartments that are neither red not black. If the ball lands on red, you get to keep the $8 you paid to play the game and you are awarded $8. If the ball lands elsewhere, you are awarded nothing and the $8 bet is collected.

What is the expected value for playing roulette if you bet $8 on red? Round your answer to the nearest cent.

Question

One option in a roulette game is to bet $8 on red. There are 18 red compartments, 18 black compartments, and two compartments that are neither red not black. If the ball lands on red, you get to keep the $8 you paid to play the game and you are awarded $8. If the ball lands elsewhere, you are awarded nothing and the $8 bet is collected.

What is the expected value for playing roulette if you bet $8 on red? Round your answer to the nearest cent.

kropot72 · Answer

Let the dollar profit be X. For a win, the profit is $8. For a loss, the profit is -$8. Setting up a probability distribution variable gives:
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$$E(X)=(-8\times \frac{20}{38})+(8\times \frac{18}{38})=you\ can\ calculate$$