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Chapter 4: Q. 72 (page 288)
You buy a lottery ticket to a lottery that costs per ticket. There are only tickets available to be sold in this lottery. In this lottery there are one prize, two prizes, and four prizes. Find your expected gain or loss.
The expected loss is.
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A consumer looking to buy a used red Miata car will call dealerships until she finds a dealership that carries the car. She estimates the probability that any independent dealership will have the car will be . We are interested in the number of dealerships she must call.
a. In words, define the random variable .
b. List the values that X may take on.
c. Give the distribution of . ~ _____(_____,_____)
d. On average, how many dealerships would we expect her to have to call until she finds one that has the car?
e. Find the probability that she must call at most four dealerships.
f. Find the probability that she must call three or four dealerships
Find the probability that her cats will wake her up no more than five times next week.
An intramural basketball team is to be chosen randomly from 15 boys and 12 girls. The team has ten slots. You want to know the probability that eight of the players will be boys. What is the group of interest and the sample?
A hospital researcher is interested in the number of times the average post-op patient will ring the nurse during a 12-hour shift. For a random sample of 50 patients, the following information was obtained. Let X = the number of times a patient rings the nurse during a 12-hour shift. For this exercise, x = 0, 1, 2, 3, 4, 5. P(x) = the probability that X takes on value x. Why is this a discrete probability distribution function (two reasons)?
There are two similar games played for Chinese New Year and Vietnamese New Year. In the Chinese version, fair dice with numbers 1, 2, 3, 4, 5, and 6 are used, along with a board with those numbers. In the Vietnamese version, fair dice with pictures of a gourd, fish, rooster, crab, crayfish, and deer are used. The board has those six objects on it, also. We will play with bets being \(1. The player places a bet on a number or object. The 鈥渉ouse鈥� rolls three dice. If none of the dice show the number or object that was bet, the house keeps the \)1 bet. If one of the dice shows the number or object bet (and the other two do not show it), the player gets back his or her \(1 bet, plus \)1 profit. If two of the dice show the number or object bet (and the third die does not show it), the player gets back his or her \(1 bet, plus \)2 profit. If all three dice show the number or object bet, the player gets back his or her \(1 bet, plus \)3 profit. Let X = number of matches and Y = profit per game.
a. In words, define the random variable X.
b. List the values that X may take on.
c. Give the distribution of X. X ~ _____(_____,_____)
d. List the values that Y may take on. Then, construct one PDF table that includes both X and Y and their probabilities.
e. Calculate the average expected matches over the long run of playing this game for the player.
f. Calculate the average expected earnings over the long run of playing this game for the player
g. Determine who has the advantage, the player or the house.
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