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 $3 on black. If the ball lands on a black number, you win $3; otherwise you lose your $3. Let X be the amount you win on your $3 bet. Then X is the random variable whose probability distribution is as follows. x 3 - 3 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. The expected value is - 0.174. (Round to three decimal places as needed.) b. On average, how much will you lose per play? You will lose an average of $ 0.174 per play. (Round to three decimal places as needed.) c. Approximately how much would you expect to lose if you bet $3 on black 100 times? 1000 times? If you bet $3 on black 100 times you would expect to lose $ . (Round to the nearest ten cents as needed.) If you bet $3 on black 1000 times you would expect to lose $ . (Round to the nearest dollar as needed.) d. Is the game profitable to play? Explain. Choose the correct answer below. A. No, the game is not profitable if you can lose money by playing it. Each time you play, you can lose $3. B. Yes, the game is profitable because you can make a profit playing the game. Each time you play, you can win $3. C. No, because the expected value of X represents the expected profit for this game. A negative number means the game is not

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 $3 on black. If the ball lands on a black number, you win $3; otherwise you lose your $3. Let X be the amount you win on your $3 bet. Then X is the random variable whose probability distribution is as follows.

x 3 - 3
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.
The expected value is - 0.174.
(Round to three decimal places as needed.)

b. On average, how much will you lose per play?
You will lose an average of $ 0.174 per play.
(Round to three decimal places as needed.)

c. Approximately how much would you expect to lose if you bet $3 on black 100 times? 1000 times?
If you bet $3 on black 100 times you would expect to lose $ .
(Round to the nearest ten cents as needed.)
If you bet $3 on black 1000 times you would expect to lose $ .
(Round to the nearest dollar as needed.)

d. Is the game profitable to play? Explain.
Choose the correct answer below.
A. No, the game is not profitable if you can lose money by playing it. Each time you play, you can lose $3.
B. Yes, the game is profitable because you can make a profit playing the game. Each time you play, you can win $3.
C. No, because the expected value of X represents the expected profit for this game. A negative number means the game is not

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 3 on black. If the ball lands on a black number, you win3; otherwise you lose your 3. Let X be the amount you win on your3 bet. Then X is the random variable whose probability distribution is as follows.

x 3 - 3
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.
The expected value is - 0.174.
(Round to three decimal places as needed.)

b. On average, how much will you lose per play?
You will lose an average of 0.174 per play.
(Round to three decimal places as needed.)

c. Approximately how much would you expect to lose if you bet3 on black 100 times? 1000 times?
If you bet 3 on black 100 times you would expect to lose .
(Round to the nearest ten cents as needed.)
If you bet 3 on black 1000 times you would expect to lose .
(Round to the nearest dollar as needed.)

d. Is the game profitable to play? Explain.
Choose the correct answer below.
A. No, the game is not profitable if you can lose money by playing it. Each time you play, you can lose 3.
B. Yes, the game is profitable because you can make a profit playing the game. Each time you play, you can win3.
C. No, because the expected value of X represents the expected profit for this game. A negative number means the game is not

Added by Meghan H.

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