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Chapter 5: Q 75. (page 330)
Rolling dice Suppose you roll two fair, six-sided dice鈥攐ne red and one green. Are the events 鈥渟um is 鈥� and 鈥済reen die shows a 鈥� independent? Justify
your answer.
Yes, independent.
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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.
Texas hold 鈥檈m In popular Texas hold 鈥檈m variety of poker, players make their best five-card poker hand by combining the two cards they are dealt with
three of five cards available to all players. You read in a book on poker that if you hold a pair (two cards of the same rank) in your hand, the probability of getting four of a kind is
(a) Explain what this probability means.
(b) Why doesn鈥檛 this probability say that if you play
1000 such hands, exactly will be four of a kind?
At the gym Suppose that of adults belong to health clubs, and of these health club members go to the club at least twice a week. What percent of all adults go to a health club at least twice a week? Write the information given in terms of probabilities, and use the general multiplication rule.
Tall people and basketball players Select an adult at random. Define events : a person is over feet tall, and : a person is a professional basketball player. Rank the following probabilities from smallest to largest. Justify your answer.
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