In the casino game of roulette, a gambler can bet on which of 38 numbers the ball will land when the roulette wheel is spun. On a $2 bet, a gambler gains $70 (so a net profit of $68) if he or she chooses the winning number, but loses the $2 otherwise. The probability of choosing the winning number is 1/38 and the probability of not choosing the winning number is 37/38. Let X denote the net gain from a roulette spin. What is the expected winnings for one spin?

Question

Mathematics

Wayne Galvan

20 January, 20:51

In the casino game of roulette, a gambler can bet on which of 38 numbers the ball will land when the roulette wheel is spun. On a $2 bet, a gambler gains $70 (so a net profit of $68) if he or she chooses the winning number, but loses the $2 otherwise. The probability of choosing the winning number is 1/38 and the probability of not choosing the winning number is 37/38. Let X denote the net gain from a roulette spin. What is the expected winnings for one spin?

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Answers (1)

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Darius Hansen · Answer 1

Expected winnings for one spin = 0.1

Step-by-step explanation:

Expected Value = Sum of [ (Probability of X) (Value of X) ]

E (X) = Σ [P (X). X]

Two Events : X = + 68, P (X) = 1/38 and X = - 2, P (X) = 37/38

E (X) = [ (68) (1/38) ] + [ (-2) (37/38) ]

[ (68) (0.03) ] + [ (-2) (0.97) ]

= 2.04 - 1.94

= 0.1