4.28 An American roulette wheel has 18 red numbers, 18 black numbers, and 2 gree Assume...

Question

Question

math Statistics-And-Probability

Answer 1

Answer #1

Given roulette wheel with 18 Red numbers, 18 Black numbers and 2 Green numbers, i.e. in all 38 numbers on a wheel.

Probability that Number appeared on wheel is Black = 18/38 =

Probability that Number appeared on wheel is Green = 02/38 =

Here if we define random variable X : Gain. Then it will take value +1 or -1

+1 if the color of betting is same as outcome color.

-1 if the color of betting is different than outcome color.

Now expected value of this game is given by

E(X) = +1 P[the color of betting is same as outcome color] -1 P[the color of betting is different than outcome color]

= 36/38 – 2/38 = 34/38 =

It means if player plays say for 100 times then he may win about 89 times.

Variance of this gain based game is

V(X) = 36/38+2/38 – (0.894737)² = 0.199446

Answer 2

Similar Homework Help Questions

An American roulette wheel contains 38 numbers: 18 are red, 18 are black, and 2 are...

An American roulette wheel contains 38 numbers: 18 are red, 18 are black, and 2 are green. When the roulette wheel is spun, the ball is equally likely to land on any of the 38 numbers. Suppose that you bet $10 on red. If the ball lands on a red number, you win $10; otherwise you lose $10. Let X = the amount that you win.
2. An American roulette wheel contains 38 numbers: 18 are red, 18 are black, and 2...

2. An American roulette wheel contains 38 numbers: 18 are red, 18 are black, and 2 are green. When the roulette wheel is spun, the ball is equally likely to land on any of the 38 numbers. Suppose that you bet $1 on red. If the ball lands on a red number, you win $1; otherwise you lose your $1. Let X be the amount you win on your $1 bet. (b) Find the expected value of the random| variable...
A roulette wheel has 38 numbers, with 18 odd numbers (black) and 18 even numbers (red),...

A roulette wheel has 38 numbers, with 18 odd numbers (black) and 18 even numbers (red), as well as 0 and 00 (which are green). If you bet $19 that the outcome is an odd number, the probability of losing the $19 is 20/38 and the probability of winning is $38 (for a net gain of only $19, given you already paid $19) is 18/38. If a player bets $19 that the outcome is an odd number, what is the...

(5.31) A roulette wheel has 38 slots, of which 18 are black, 18 are red, and...

(5.31) A roulette wheel has 38 slots, of which 18 are black, 18 are red, and 2 are green. When the wheel is spun, the ball is equally likely to come to rest in a any of the slots. Gamblers can place a number of different bets in roulette. One of the simplest wagers chooses red or black. A bet of $1 on red will pay off an additional dollar if the ball lands in a red slot. Otherwise, the...
In the American version of the Game Roulette, a wheel has 18 black slots, 8 red...

In the American version of the Game Roulette, a wheel has 18 black slots, 8 red slots and 2 green slots. All slots are the same size. In a carnival game, a person wagers $2 on the roll of two dice. A person can wager on either red or black. Green is reserved for the house. If a player wagers $5 on either red or black and that color comes up, they win $10 otherwise they lose their wager. What is the expected value of...
in a game of roulette, there are 18 red numbers, 18 black numbers, and 2 green numbers

in a game of roulette, there are 18 red numbers, 18 black numbers, and 2 green numbers. you may bet on red or black, but not green. if you win a $1 bet on the color, the house pays you $1. what is the expected value of each $1 you play at this game

2. (From the Fall 2017 takehome.) In American roulette, a roulette wheel with 38 possible outcomeste...

2. (From the Fall 2017 takehome.) In American roulette, a roulette wheel with 38 possible outcomeste numbers 1 to 36, "0", and "00" is spun. As the wheel spins, players makes bets on which number the ball w land on. Eventually the wheel stops, and a ball lands randomly on one of the 38 numbers, with an equal probability for each one. A statistics professor's father bets that the wheel wil land on one of the numbers from 1 to...
In roulette, the numbers from 1 to 36 are evenly distributed between red and black. A...

In roulette, the numbers from 1 to 36 are evenly distributed between red and black. A player who bets $1 on black wins $1 (and gets the $1 bet back) if the ball comes to rest on black; otherwise (if the ball lands on red, 0, or 00), the $1 bet is lost. One option in a roulette game is to bet $11 on red. If the ball lands on red, you get to keep the $11 you paid to...
In roulette, the numbers from 1 to 36 are evenly distributed between red and black. A...

In roulette, the numbers from 1 to 36 are evenly distributed between red and black. A player who bets $1 on black wins $1 (and gets the $1 bet back) if the ball comes to rest on black; otherwise (if the ball lands on red, 0, or 00), the $1 bet is lost. One option in a roulette game is to bet $17 on red. If the ball lands on red, you get to keep the $17 you paid to...

Problem 3 (Quiz). Recall that an American Roulette wheel has 38 possible outcomes, 18 black, 18...

Problem 3 (Quiz). Recall that an American Roulette wheel has 38 possible outcomes, 18 black, 18 red and 2 green. The numbers go from 1 to 36, and the green outcomes are numbered 0 and 00. Someone places İO bets on "1st 12", that is, that person wins if the outcome is any number between 1 and 12, included. 1. What is the probability of losing 8 out of the 10 total bets?