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.

(a) If you bet on "red," you win if the ball lands in a red slot. What is the probability of winning with a bet on red in a single play of roulette? (Enter your answer rounded to five decimal places.)

probability =

(b) You decide to play roulette 8 times, each time betting on red. What is the distribution of X , the number of times you win?

Normal distribution with μ=38 and σ=0.52356

binomial distribution with n=38 and p=0.52356

Normal distribution with μ=8 and σ=0.47368

Normal distribution with μ=18 and σ=47.02314

binomial distribution with n=8 and p=0.47368

binomial distribution with n=18 and p=47.02314

What is the mean of X ? (Enter your answer rounded to five decimal places.)

mean of X=

What is the standard deviation of X ? (Enter your answer rounded to five decimal places).

standard deviation of X=

(c) If you bet the same amount on each play and win on exactly 44 of the 88 plays, you will "break even." What is the probability that you will break even? (Enter your answer rounded to five decimal places.)

P(X=4)=

(d) If you win on fewer than 4 of the 8 plays, you will lose money. What is the probability that you will lose money? (Enter your answer rounded to five decimal places.)

P(X<4)=

Answer 1

a) probability of winning with a bet on red in a single play of roulette =18/38 =0.47368

binomial distribution with n=8 and p=0.47368

mean E(x)=μ=np=3.78947

standard deviation σ=√(np(1-p))=1.41225

c)

P(X=4)=

(nCx)px(1−p)(n-x)    =

0.27042

d)

P(X<4)=

∑x=04     (nCx)px(1−p)(n-x)    =

0.42220