In roulette there are 38 equally likely possibilities: the numbers 1-36, 0, and

Question

In roulette there are 38 equally likely possibilities: the numbers 1-36, 0, and 00. What is the expected value for a gambler who bets $1 on number 15 if she wins $35 each time the number 15 turns up and loses $1 if any other number turns up? If the gambler plays the number 15 for 200 consecutive times, what is the total expected gain? In roulette there are 38 equally likely possibilities: the numbers 1-36,0, and 00 (double zero). See the figure. What is the expected value for a gambler who bets $1 on number 15 if she wins $35 each time the number 15 turns up and loses $1 if any other number turns up? If the gambler plays the number 15 for 200 consecutive times, what is the total expected gain? Page

Explanation / Answer

probabilty of number 15 to come =1/38

hence expected value for a game =expected prize -ticket cost =(1/38)*35-1=$(-3/38)

total expected gain for 200 plays =200*-3/38 =$-15.79

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