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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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Sampling senators Refer to Exercise 50.
(a) Construct a Venn diagram that models the chance process using events R: is a Republican, and F: is female.
(b) Find Interpret this value in context.
(c) Find Interpret this value in context.
Lotto In the United Kingdom’s Lotto game, a player picks six numbers from 1 to 49 for each ticket. Rosemary bought one ticket for herself and one for each of her four adult children. She had the lottery computer randomly select the six numbers on each ticket. When the six winning numbers were drawn, Rosemary was surprised to find that none of these numbers appeared on any of the five Lotto tickets she had bought. Should she be? Design and carry
out a simulation to answer this question. Follow the four-step process.
During World War II, the British found that the probability that a bomber is lost through enemy action on a mission over occupied Europe was Assuming that missions are independent, find the probability that a bomber returned safely from missions.
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’t foolproof—sometimes it suggests that a person is lying when they’re actually telling the truth (a “false positive”). Other times, the test says that the suspect is being truthful when the person is actually lying (a “false negative”). 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.
Mac or PC? A recent census at a major university revealed that of its students primarily used Macintosh computers (Macs). The rest mainly used
PCs. At the time of the census, of the school’s students were undergraduates. The rest were graduate students. In the census, of respondents were graduate students who said that they used PCs as their
main computers. Suppose we select a student at random from among those who were part of the census.
(a) Assuming that there were students in the census, make a two-way table for this chance process.
(b) Construct a Venn diagram to represent this setting.
(c) Consider the event that the randomly selected student is a graduate student who uses a Mac. Write this event in symbolic form using the two events of interest that you chose in (b).
(d) Find the probability of the event described in (c). Explain your method.
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