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Chapter 5: Q. 47 (page 328)
Dogs and cats In one large city, of all households own a dog, own a cat, and own both. Suppose we randomly select a household. What’s the probability that the household owns a dog or a cat?
The likelihood that the household owns either a dog or a cat is
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Mystery box Ms. Tyson keeps a Mystery Box in her classroom. If a student meets expectations for behavior, she or he is allowed to draw a slip of paper without looking. The slips are all of equal size, are well mixed, and have the name of a prize written on them. One of the “prizes”—extra homework—isn’t very desirable! Here is the probability model for the prizes a student can win:
a. Explain why this is a valid probability model.
b. Find the probability that a student does not win extra homework.
c. What’s the probability that a student wins candy or a homework pass?
Is this your card? A standard deck of playing cards (with jokers removed) consists of 52 cards in four suits—clubs, diamonds, hearts, and spades. Each suit has 13 cards, with denominations ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. The jacks, queens, and kings are referred to as “face cards.” Imagine that we shuffle the deck thoroughly and deal one card. The two-way table summarizes the sample space for this chance process based on whether or not the card is a face card and whether or not the card is a heart.
| Type of card | |||
| Face card | Non-Face card | Total | |
| Heart | |||
| Non-Heart | |||
| Total | |||
Are the events “heart” and “face card” independent? Justify your answer.
Liar, liar! Sometimes police use a lie detector test to help determine whether a suspect is
telling the truth. A lie detector test isn’t foolproof—sometimes it suggests that a person is
lying when he or she is actually telling the truth (a “false positive”). Other times, the test
says that the suspect is being truthful when he or she is actually lying (a “false negative”).
For one brand of lie detector, the probability of a false positive is 0.08.
a. Explain what this probability means.
b. Which is a more serious error in this case: a false positive or a false negative? Justify
your answer.
Tall people and basketball players Select an adult at random. Define events T: person is over feet tall, and
B: person is a professional basketball player. Rank the following probabilities from smallest to largest. Justify your answer.
Random assignment Researchers recruited volunteers-men and women-to take part in an experiment. They randomly assigned the subjects into two groups of people each. To their surprise, of the men were randomly assigned to the same treatment. Should they be surprised? We want to design a simulation to estimate the probability that a proper random assignment would result in or more of the men ending up in the same group.
Get identical slips of paper. Write "" on of the slips and "" on the remaining slips. Put the slips into a hat and mix well. Draw of the slips without looking and place into one pile representing Group . Place the other slips in a pile representing Group . Record the largest number of men in either of the two groups from this simulated random assignment. Repeat this process many, many times. Find the percent of trials in which or more men ended up in the same group.
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