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Chapter 5: Q 73. (page 330)
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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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.
Treating low bone density (4.2) Fractures of the spine are common and serious among women with advanced osteoporosis (low mineral density in the
bones). Can taking strontium ranelate help? A large medical trial assigned 1649 women to take either strontium ranelate or a placebo each day. All of
the subjects had osteoporosis and had had at least one fracture. All were taking calcium supplements and receiving standard medical care. The response variables were measurements of bone density and counts of new fractures over three years. The subjects were treated at medical centers in different countries. Outline an appropriate design for this experiment. Explain why this is the proper design.
Fill 鈥檈rr up! In a recent month, of automobile drivers filled their vehicles with regular gasoline, purchased midgrade gas, and bought premium gas. Of those who bought regular gas, paid with a credit card; of customers who bought midgrade and premium gas, and , respectively, paid with a credit card. Suppose we select a customer at random.
Draw a tree diagram to represent this situation. What鈥檚 the probability that the customer paid with a credit card? Use the four-step process to guide your work.
Roulette, An American roulette wheel hasslots with numbers through as shown in the figure. Of the numbered slots, are red, are black, and 鈥攖丑别 and 鈥攁re green. When the wheel is spun, a metal ball is dropped onto the middle of the wheel. If the wheel is balanced, the ball
is equally likely to settle in any of the numbered slots. Imagine spinning a fair wheel once. Define events B: ball lands in a black slot, and E: ball lands in an even numbered slot. (Treat and as even numbers.)
(a) Make a two-way table that displays the sample space in terms of events B and E.
(b) Find P(B) and P(E).
(c) Describe the event 鈥淏 and E鈥� in words. Then find P(B and E). Show your work.
(d) Explain why P(B or E) 鈮� P(B) + P(E). Then use the general addition rule to compute P(B or E).
Late shows Some TV shows begin after their scheduled times when earlier programs run late. According to a network鈥檚 records, about 3% of its shows start late. To find the probability that three consecutive shows on this network start on time, can we multiply (0.97)(0.97)(0.97)? Why or why not?
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