A game of chance is played on a wheel that contains 40numbers (19 are red, 19 are black, and 2 are green). When the wheel is spun, the ball is equally likely to land on any of the 40 numbers. Suppose that you bet $9 on black. If the ball lands on a black number, you win $9; otherwise you lose your $9. Let X be the amount you win on your $9 bet. Then X is the random variable whose probability distribution is as follows. x 9 −9 P(X=x) 0.475 0.525 Use this to complete parts (a) through (d) to the right. a. Find the expected value of the random variable X. The expected value is (Round to three decimal places as needed.) b. On average, how much will you lose per play? You will lose an average of $ per play. (Round to three decimal places as needed.) c. Approximately how much would you expect to lose if you bet $9 on black 100 times? 1000 times? If you bet $9 on black 100 times you would expect to lose $ (Round to the nearest ten cents as needed.) If you bet $9 on black 1000 times you would expect to lose $ (Round to the nearest dollar as needed.) d. Is the game profitable to play? Explain.
A game of chance is played on a wheel that contains 40numbers (19 are red, 19 are black, and 2 are green). When the wheel is spun, the ball is equally likely to land on any of the 40 numbers. Suppose that you bet $9 on black. If the ball lands on a black number, you win $9; otherwise you lose your $9. Let X be the amount you win on your $9 bet. Then X is the random variable whose probability distribution is as follows. x 9 −9 P(X=x) 0.475 0.525 Use this to complete parts (a) through (d) to the right. a. Find the expected value of the random variable X. The expected value is (Round to three decimal places as needed.) b. On average, how much will you lose per play? You will lose an average of $ per play. (Round to three decimal places as needed.) c. Approximately how much would you expect to lose if you bet $9 on black 100 times? 1000 times? If you bet $9 on black 100 times you would expect to lose $ (Round to the nearest ten cents as needed.) If you bet $9 on black 1000 times you would expect to lose $ (Round to the nearest dollar as needed.) d. Is the game profitable to play? Explain.
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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Question
A game of chance is played on a wheel that contains 40numbers (19 are red, 19 are black, and 2 are green). When the wheel is spun, the ball is equally likely to land on any of the 40 numbers. Suppose that you bet $9 on black. If the ball lands on a black number, you win $9; otherwise you lose your $9. Let X be the amount you win on your $9 bet. Then X is the random variable whose probability distribution is as follows.
|
x
|
9 |
−9
|
|
P(X=x)
|
0.475
|
0.525
|
Use this to complete parts (a) through (d) to the right.
a. Find the expected value of the random variable X.
The expected value is
(Round to three decimal places as needed.)
b.
On average, how much will you lose per play?You will lose an average of
$
per play.(Round to three decimal places as needed.)
c. Approximately how much would you expect to lose if you bet $9 on black 100 times? 1000 times?
If you bet $9 on black 100 times you would expect to lose
$
(Round to the nearest ten cents as needed.)
If you bet $9 on black 1000 times you would expect to lose
$
(Round to the nearest dollar as needed.)
d.
Is the game profitable to play? Explain.Expert Solution
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