A roulette wheel has 38 slots, numbered 0, 00, and 1 to 36. The slots 0 and 00 a

Question

A roulette wheel has 38 slots, numbered 0, 00, and 1 to 36. The slots 0 and 00 are colored green, 18 of the others are red, and 18 are black. The dealer spins the wheel and at the same time rolls a small ball along the wheel in the opposite direction. The wheel is carefully balanced so that the ball is equally likely to land in any slot when the wheel slows. Gamblers can bet on various combinations of numbers and colors.

You decide to play roulette 400 times, each time betting the same amount on red. You will lose money if you win on fewer than 200 of the plays. What is the probability that you will lose money? (Check that the Normal approximation is permissible, and use it to find this probability. Round your answer to four decimal places.)

Explanation / Answer

p = 18/38 = 9/19

q = 10/19

n = 400

Mean = np = 400x9/19 = 189.47

Standard deviation = sq root(npq) = (400x(9/19)(10/19))0.5 = 9.99

P(you will lose money) = P(X<200)

= P(Z < (200 - mean)/standard deviation)

= P(Z < (200 - 189.47)/9.99)

= P(Z < 1.05)

= 0.8531

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