Question 102628: A roulette wheel in the U.S. has 18 red slots, 18 black slots and 2 green slots. You can bet $1 on either red or black. I fyou win, you get your $1 back plus an additional $1. If you lose, you lose your $1 bet. What are your expected winnings on one spin of the wheel (include the variance and standard deviation for all)? Two successive 1$ bets on the wheel? A single $2 bet? 100 successive $1 bets?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A roulette wheel in the U.S. has 18 red slots, 18 black slots and 2 green slots. You can bet $1 on either red or black. If you win, you get your $1 back plus an additional $1. If you lose, you lose your $1 bet. What are your expected winnings on one spin of the wheel (include the variance and standard deviation for all)? Two successive 1$ bets on the wheel? A single $2 bet? 100 successive $1 bets?
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Random Variable (winnings): $1, -$1
Associated probabilities:
P($1) = 18/38 =9/19
P(-1) = 20/38 = 10/19
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Expected winnings is (9/19)*1 + (10/19)*-1
= -1/19 cents on one spin.
= -2/19 cents on two spins
= -2/19 cents on a single spin for $2
= -100/19 cents on 100 successive spins
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Cheers,
Stan H.
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