Chapter 4: Q.69 (page 288)
Is it likely that there will be more than 20 teens killed from motor vehicle injuries on any given day in the U.S.? Justify your answer numerically.
No, it is not likely that there will be 20 teens killed from motor vehicle injuries on any given day in the U.S.
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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 \(1. The player places a bet on a number or object. The “house” rolls three dice. If none of the dice show the number or object that was bet, the house keeps the \)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.
You are playing a game of chance in which four cards are drawn from a standard deck of 52 cards. You guess the suit of each card before it is drawn. The cards are replaced in the deck on each draw. You pay \(1 to play. If you guess the right suit every time, you get your money back and \)256. What is your expected profit of playing the game over the long term?
Construct a PDF table.
On average, Pierre, an amateur chef, drops three pieces of egg shell into every two cake batters he makes. Suppose
that you buy one of his cakes.
a. In words, define the random variable .
b. List the values that may take on.
c. Give the distribution of
d. On average, how many pieces of egg shell do you expect to be in the cake?
e. What is the probability that there will not be any pieces of egg shell in the cake?
f. Let’s say that you buy one of Pierre’s cakes each week for six weeks. What is the probability that there will not
be any egg shell in any of the cakes?
g. Based upon the average given for Pierre, is it possible for there to be seven pieces of shell in the cake? Why?
On average, how many years would you expect a physics major to spend doing post-graduate research?
Use the following information to answer the next seven exercises: A ballet instructor is interested in knowing what percent
of each year's class will continue on to the next, so that she can plan what classes to offer. Over the years, she has established
the following probability distribution.
• Let the number of years a student will study ballet with the teacher.
• Let the probability that a student will study ballet x years.
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