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Chapter 5: Q. 69. (page 330)
Dogs and cats In one large city, of all households, own a dog,
own a cat, and 18% own both. Suppose we randomly select a household and learn that the household owns a cat. Find the probability that the household owns a dog.
The probability that the household owns a dog is
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Three machines鈥擜, B, and C鈥攁re used to produce a large quantity of identical parts at
a factory. Machine A produces of the parts, while Machines B and C produce
and of the parts, respectively. Historical records indicate that of the parts
produced by Machine A are defective, compared with for Machine B, and for
Machine C. Suppose we randomly select a part produced at the factory.
a. Find the probability that the part is defective.
b. If the part is inspected and found to be defective, what鈥檚 the probability that it was
produced by Machine B?
Cell phones The Pew Research Center asked a random sample of adult cell-phone owners from the United States their age and which type of cell phone they own: iPhone, Android, or other (including non-smartphones). The two-way table summarizes the data.
Suppose we select one of the survey respondents at random.
An unenlightened gambler
a. A gambler knows that red and black are equally likely to occur on each spin of a
roulette wheel. He observes that consecutive reds have occurred and bets heavily on
black at the next spin. Asked why, he explains that 鈥渂lack is due.鈥� Explain to the
gambler what is wrong with this reasoning.
b. After hearing you explain why red and black are still equally likely after reds on the
roulette wheel, the gambler moves to a card game. He is dealt straight red cards from
a standard deck withred cards and black cards. He remembers what you said and
assumes that the next card dealt in the same hand is equally likely to be red or black.
Explain to the gambler what is wrong with this reasoning.
Recycling Do most teens recycle? To find out, an AP庐 Statistics class asked an SRS of students at their school whether they regularly recycle. In the sample, students said that they recycle. Is this convincing evidence that more than half of the students at the school would say they regularly recycle? The dotplot shows the results of taking SRSS of students from a population in which the true proportion who recycle is .
a. Explain why the sample result (out of said "Yes") does not give convincing evidence that more than half of the school's students recycle.
b. Suppose instead that students in the class's sample had said "Yes." Explain why this result would give convincing evidence that a majority of the school's students recycle.
AARP, and Medicare (4.1) To find out what proportion of Americans support proposed
Medicare legislation to help pay medical costs, the AARP conducted a survey of their
members (people over age who pay membership dues). One of the questions was:
鈥淓ven if this plan won鈥檛 affect you personally either way, do you think it should be passed
so that people with low incomes or people with high drug costs can be helped?鈥� Of the
respondents, answered 鈥淵es.鈥�
a. Describe how undercoverage might lead to bias in this study. Explain the likely
direction of the bias.
b. Describe how the wording of the question might lead to bias in this study. Explain the
likely direction of the bias.
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