A roulette wheel has slots marked with the numbers from 1 to 36 aswell as 0 and

Question

A roulette wheel has slots marked with the numbers from 1 to 36 aswell as 0 and 00 (the latter is called "double zero"). With eachspin of the wheel, the ball lands in one of these 38 slots.

Half of the slots marked 1 to 36 are colored red and the other halfare black. So if Mike bets on "red", he wins if the outcome is oneof the 18 red outcomes, and he loses if the outcome is one of the18 black outcomes or is 0 or 00. So there are 18 outcomes in whichMike wins and 20 outcomes in which he loses. Therefore Mike'sprobability of winning is 18/38 or 9/19 if he bets on red. If hewins, then the payoff is equal to the amount of money he bets. Ifhe loses, then he loses the money he bets.

Mike goes to the casino with $800 and decides to bet $75 on red.What is the expected value for the amount of money he will haveafter he has made this bet (and either won or lost)? (Give youranswer in $ without including the "$" symbol. Your answer should beaccurate to the nearest cent.)

Explanation / Answer

If he plays one game then the expected value is just the sumof the weighted means, so....
expected value=the amount he will have if he wins X theprobability of success + the amount he will lose if he loses X theprobability of a loss
75.00(9
9) + 0.00(10
9) = 35.53
If he only plays once then itsjust (800-75) + 35.53= 760.53

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