Probability

Please explain!

A roulette wheel used in a US casino has 38 slots, of which 18 are red, 18 are black and 2 green. A roulette wheel in a French casino has 37 slots, 18 red 18 black and 1 green. A ball is rolles around the wheel and ends up in one of the slots with equal probability. Suppose that a player bets on red. iF A $1 bet is placed, the player wins $1 if the ball hits a red slot (the player's $1 bet is returned). If the ball ends up in a black or green slot, the $1 bet is lost

Find the expected value of this game to the player in
a) the US
b) France

Quote:

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Originally Posted by amor_vincit_omnia

Please explain!

A roulette wheel used in a US casino has 38 slots, of which 18 are red, 18 are black and 2 green. A roulette wheel in a French casino has 37 slots, 18 red 18 black and 1 green. A ball is rolles around the wheel and ends up in one of the slots with equal probability. Suppose that a player bets on red. iF A $1 bet is placed, the player wins $1 if the ball hits a red slot (the player's $1 bet is returned). If the ball ends up in a black or green slot, the $1 bet is lost

Find the expected value of this game to the player in
a) the US
b) France

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Let p be the probability of the ball landing on red and let X be the random variable amount of money won on a single spin of the wheel.

The E(X) = (1)(p) + (-1)(1 - p) = 2p - 1.