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Chapter 5: Q 85. (page 331)
Fill 鈥檈r up Refer to Exercise 83. Given that the customer paid with a credit card, find the probability that she bought premium gas.
The probability that she bought premium gas is
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Spinning a quarter With your forefinger, hold a new quarter (with a state featured on the reverse) upright, on its edge, on a hard surface. Then flick it with your other forefinger so that it spins for some time before it falls and comes to rest. Spin the coin a total of 25 times, and record the results.
(a) What鈥檚 your estimate for the probability of heads? Why?
(b) Explain how you could get an even better estimate.
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.
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.
Mac or PC? A recent census at a major university revealed that 40% of its students mainly used Macintosh computers (Macs). The rest mainly used
PCs. At the time of the census, of the school鈥檚 students were undergraduates. The rest were graduate students. In the census, of the respondents were graduate students who said that they used PCs as their
primary computers. Suppose we select a student at random from among those who were part of the census and learn that the student mainly uses a Mac.
Find the probability that this person is a graduate student. Show your work.
Free throws A basketball player has probability of making a free throw. Explain how you would use each chance device to simulate one free throw by the player.
(a) A six-sided die
(b) Table D of random digits
(c) A standard deck of playing cards
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