In​ roulette, the numbers from 1 to 36 are evenly distributed between red and black. A player who bets​ $1 on black wins​ $1 (and gets the​ $1 bet​ back) if the ball comes to rest on​ black; otherwise​ (if the ball lands on​ red, 0, or​ 00), the​ $1 bet is lost. One option in a roulette game is to bet $8 on red. If the ball lands on​ red, you get to keep the $8 you paid to play the​ game, and you are awarded ​$9. If the ball lands​ elsewhere, you are awarded​ nothing, and the $8 that you bet is collected. What is the expected value of the​ game?

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Chapter1: Combinatorial Analysis
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In​ roulette, the numbers from 1 to 36 are evenly distributed between red and black. A player who bets​ $1 on black wins​ $1 (and gets the​ $1 bet​ back) if the ball comes to rest on​ black; otherwise​ (if the ball lands on​ red, 0, or​ 00), the​ $1 bet is lost. One option in a roulette game is to bet

$8

on red. If the ball lands on​ red, you get to keep the

$8

you paid to play the​ game, and you are awarded

​$9.

If the ball lands​ elsewhere, you are awarded​ nothing, and the

$8

that you bet is collected. What is the expected value of the​ game?

In roulette, the numbers from 1 to 36 are evenly distributed between red and black. A player who bets $1 on black wins $1 (and gets the $1 bet back) if the ball comes to rest on black; otherwise (if the ball lands on red, 0, or 00), the $1 bet is lost.
One option in a roulette game is to bet $8 on red. If the ball lands on red, you get to keep the $8 you paid to play the game, and you are awarded $9. If the ball lands elsewhere, you are awarded nothing, and the $8 that you bet is collected. What
is the expected value of the game?
The expected value for playing roulette if you bet $8 on red is approximately $
(Round to the nearest cent as needed.)
Transcribed Image Text:In roulette, the numbers from 1 to 36 are evenly distributed between red and black. A player who bets $1 on black wins $1 (and gets the $1 bet back) if the ball comes to rest on black; otherwise (if the ball lands on red, 0, or 00), the $1 bet is lost. One option in a roulette game is to bet $8 on red. If the ball lands on red, you get to keep the $8 you paid to play the game, and you are awarded $9. If the ball lands elsewhere, you are awarded nothing, and the $8 that you bet is collected. What is the expected value of the game? The expected value for playing roulette if you bet $8 on red is approximately $ (Round to the nearest cent as needed.)
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