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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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Brushing teeth, wasting water? A recent study reported that fewer than half of young adults turn off the water while brushing their teeth. Is the same true for teenagers? To find out, a group of statistics students asked an SRS of 60 students at their school if they usually brush with the water off. How many
students in the sample would need to say 鈥淣o鈥� to provide convincing evidence that fewer than half of the students at the school brush with the water off? The Fathom dot plot below shows the results of taking 200 SRSs of 60 students from a population in which the true proportion who brush with the
water off is 0.50.
(a) Suppose 27 students in the class鈥檚 sample say 鈥淣o.鈥� Explain why this result does not give convincing evidence that fewer than half of the school鈥檚 students brush their teeth with the water off.
(b) Suppose 18 students in the class鈥檚 sample say 鈥淣o.鈥� Explain why this result gives strong evidence that fewer than 50% of the school鈥檚 students brush
their teeth with the water off.
Sampling senators The two-way table describes the members of the U.S. Senate in a recent year. Suppose we select a senator at random. Consider events D: is a democrat, and F: is female.
(a) Find P(D | F). Explain what this value means.
(b) Find P(F | D). Explain what this value means.
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?
Urban voters The voters in a large city are white, black, and Hispanic. (Hispanics may be of any race in official statistics, but here we are speaking of political blocks.) A mayoral candidate anticipates attracting of the white vote, of the black vote, and of the Hispanic vote. Draw a tree diagram to represent this situation. What percent of the overall vote does the candidate expect to get? Use the four-step process to guide your work.
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.
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