A game of chance is played on a wheel that contains 34 numbers (16 are red,16 are black, and 2 are green). When the wheel is spun, the ball is equally likely to land on any of the 34 numbers. Suppose that you bet $4 on red. If the ball lands on a red number, you win $4; otherwise, you lose your $4. Let X be the amount you win on your $4 bet. Then X is the random variable whose probability distribution is as follows.
A game of chance is played on a wheel that contains 34 numbers (16 are red,16 are black, and 2 are green). When the wheel is spun, the ball is equally likely to land on any of the 34 numbers. Suppose that you bet $4 on red. If the ball lands on a red number, you win $4; otherwise, you lose your $4. Let X be the amount you win on your $4 bet. Then X is the random variable whose probability distribution is as follows.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
A game of chance is played on a wheel that contains 34 numbers
(16 are red,16 are black, and 2 are green). When the wheel is spun, the ball is equally likely to land on any of the 34 numbers. Suppose that you bet $4
on red. If the ball lands on a red number, you win $4; otherwise, you lose your $4. Let X be the amount you win on your $4 bet. Then X is the random variable whose probability distribution is as follows.|
x
|
4
|
−4
|
|
P(X=x)
|
0.471
|
0.529
|
Use this to complete parts (a) through (d) to the right.
a. Find the expected value of the random variable X.
(Round to three decimal places as needed.)
b.
On average, how much will you lose per play?(Round to three decimal places as needed.
c. Approximately how much would you expect to lose if you bet $4 on red 100 times? and 1000 times?
(Round to the nearest dollar as needed.)
d.
Is the game profitable to play? Explain.Choose the correct answer below.
No, the game is not profitable if you can lose money by playing it. Each time you play, you can lose
$4.
Yes, the game is profitable because you can make a profit playing the game. Each time you play, you can win $4.
No, because the expected value of X represents the expected profit for this game. A negative number means the game is not profitable.
Yes, because the average profit per game is positive.
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