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Chapter 5: Q 108. (page 333)
BMI (5.2) Suppose we select two American young women in this age group at random. Find the probability that at least one of them is classified as underweight. Show your work.
P (at least one of two underweight) =
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Urban voters In the election described in Exercise 84, if the candidate鈥檚 predictions come true, what percent of her votes come from black voters? (Write this as a conditional probability and use the definition of conditional probability.)
Income tax returns Here is the distribution of the adjusted gross income (in thousands of dollars) reported on individual federal income tax returns
in a recent year:
(a) What is the probability that a randomly chosen return shows an adjusted gross income of or more?
(b) Given that a return shows an income of at least what is the conditional probability that the income is at least
Rolling a die The following figure displays several possible probability models for rolling a die. We can learn which model is actually accurate for a particular die only by rolling the die many times. However, some of the models are not legitimate. That is, they do not obey the rules. Which are legitimate and which are not? In the case of the illegitimate models, explain what is wrong.
Tossing coins Imagine tossing a fair coin times. (a) What is the sample space for this chance
process? (b) What is the assignment of probabilities to outcomes in this sample space?
Liar, liar! Sometimes police use a lie detector (also known as a polygraph) to help determine whether a suspect is telling the truth. A lie detector test isn鈥檛 foolproof鈥攕ometimes it suggests that a person is lying when they鈥檙e actually telling the truth (a 鈥渇alse positive鈥�). Other times, the test says that the suspect is being truthful when the person is actually lying (a 鈥渇alse negative鈥�). For one brand of polygraph machine, the probability of a false positive is .
(a) Interpret this probability as a long-run relative frequency.
(b) Which is a more serious error in this case: a false positive or a false negative? Justify your answer.
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