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​ $1 bet is lost. One option in a roulette game is to bet$ 3on red. If the ball lands on​ red, you get to keep the $ 3you paid to play the​ game, and you are awarded$4.If the ball lands​ elsewhere, you are awarded​ nothing, and the$ 3 that you bet is collected. What is the expected value of the​ game?

Question

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​ $1 bet is lost. One option in a roulette game is to bet$ 3on red. If the ball lands on​ red, you get to keep the $ 3you paid to play the​ game, and you are awarded$4.If the ball lands​ elsewhere, you are awarded​ nothing, and the$ 3 that you bet is collected. What is the expected value of the​ game?

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