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 decided to play roulette 200 times, each time betting the same amount on red. You will lose money if you win on fewer than 100 of the plays. What is the probability that you will lose money? (Check the normal approximation is permissible and use it to find this probablilty.

Explanation / Answer

decided to play roulette 200 times

given n = 200,

p = 18/38 = 9/19, q = 1-10/19
lesser of np & nq = 200*9/19 = 94.7, so normal approximation definitely possible !

You will lose money if you win on fewer than 100 of the plays

P(<100), applying continuity correction, it becomes

P(<99.5)
= (n p) = 94.7368; ² = ( n p q ) = 49.8615; = ( n p q ) = 7.0613
z = ( x - ) / = 0.6745
P (x < 99.5000) = P (z < 0.6745) = 0.7500

the probability that you will lose money is 0.750

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