question archive A game of chance is played on a wheel that contains 40 numbers (19 are red, 19 are black, and 2 are green)
A game of chance is played on a wheel that contains 40 numbers (19 are red, 19 are black, and 2 are green)
Subject:StatisticsPrice: Bought3
A game of chance is played on a wheel that contains 40 numbers (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 $4 on black. If the ball lands on a black number, you win $4; othenivise 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) 0.475 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 I: . (Round to three decimal places as needed.) b. On average, how much wi I you lose per play? You will lose an average of $ :I per play. (Round to three decimal places as needed.) 1:. Approximately how much would you expect to lose if you bet $4 on black 100 times? 1000 times? If you bet $4 on black 100 times you would expect to lose $I: . (Round to the nearest ten cents as needed.) If you bet $4 on black 1000 times you would expect to lose $|:|. (Round to the nearest dollar as needed.)
d. Is the game pro?table to play? Explain. Choose the correct answer below. 0 A. Yes, because the average pro?t per game is positive. O B. Yes, the game is pro?table because you can make a pro?t playing the game. Each time you play, you can win $4. O C. No, the game is not pro?table if you can lose money by playing it. Each time you play, you can lose $4. O D. No, because the expected value of X represents the expected pro?t for this game. A negative number means the game is not pro?table.
