Problem 1
Coin toss. Is a coin flip random? Why or why not?
Problem 2
Casino. A casino claims that its electronic "video roulette" machine is truly random. What should that claim mean?
Problem 4
Games. Many kinds of games people play rely on randomness. Cite three different methods commonly used in the attempt to achieve this randomness, and discuss the effectiveness of each.
Problem 5
Birth defects. The American College of Obstetricians and Gynecologists says that out of every 100 babies born in the United States. 3 have some kind of major birth defect. How would you assign random numbers to conduct a simulation based on this statistic?
Problem 6
Colorblind. By some estimates, about \(10 \%\) of all males have some color perception defect, most commonly redgreen colorblindness. How would you assign random numbers to conduct a simulation based on this statistic?
Problem 9
Play the lottery. Some people play state-run lotteries by always playing the same favorite "lucky" number. Assuming that the lottery is truly random, is this strategy better, worse, or the same as choosing different numbers for each play? Explain.
Problem 11
Bad simulations. Explain why each of the following simulations fails to model the real situation properly: a) Use a random integer from 0 through 9 to represent the number of heads when 9 coins are tossed. b) A basketball player takes a foul shot. Look at a random digit, using an odd digit to represent a good shot and an even digit to represent a miss. c) Use random digits from 1 through 13 to represent the denominations of the cards in a five-card poker hand.
Problem 12
More bad simulations. Explain why each of the following simulations fails to model the real situation: a) Use random numbers 2 through 12 to represent the sum of the faces when two dice are rolled. b) Use a random integer from 0 through 5 to represent the number of boys in a family of 5 children. c) Simulate a baseball player's performance at bat by letting \(0=\) an out, \(1=\) a single, \(2=\) a double, \(3=\) a triple, and \(4=\) a home run.
Problem 13
Wrong conclusion. A Statistics student properly simulated the length of checkout lines in a grocery store and then reported, "The average length of the line will be \(3.2\) people." What's wrong with this conclusion?
Problem 16
Two pair or three of a kind? When drawing five cards randomly from a deck, which is more likely, two pairs or three of a kind? A pair is exactly two of the same denomination. Three of a kind is exactly 3 of the same denomination. (Don't count three \(8^{\prime}\) s as a pair-that's 3 of a kind. And don't count 4 of the same kind as two pair-that's 4 of a kind, a very special hand.) How could you simulate 5-card hands? Be careful; once you've picked the 8 of spades, you can'\operatorname{tg} e t ~ i t ~ a g a i n ~ i n ~ t h a t ~ h a n d . ~ a) Describe how you will simulate a component. b) Describe how you will simulate a trial. c) Describe the response variable.
