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Chapter 5: Q 86. (page 331)
Urban voters In the election described in Exercise 84, if the candidate鈥檚 predictions come true, what percent of her votes come from black voters? (Write this as a conditional probability and use the definition of conditional probability.)
The percentage of her votes comes from black voters is
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Late flights An airline reports that 85% of its flights arrive on time. To find the probability that its next four flights into LaGuardia Airport all arrive on time, can
we multiply (0.85)(0.85)(0.85)(0.85)? Why or why not?
Bright lights? A string of Christmas lights contains lights. The lights are wired in series so that if any light fails the whole string will go dark. Each light
has a probability of failing during a-year period. The lights fail independently of each other. Find the probability that the string of lights will remain bright for years.
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).
Recycling Do most teens recycle? To find out, an AP Statistics class asked an SRS of 100 students at their school whether they regularly recycle. How many students in the sample would need to say 鈥淵es鈥� to provide convincing evidence that more than half of the students at the school recycle? The Fathom dot plot below shows the results of taking 200 SRSs of 100 students from a population in which the true proportion who recycle is 0.50.
(a) Suppose 55 students in the class鈥檚 sample say 鈥淵es.鈥� Explain why this result does not give convincing evidence that more than half of the school鈥檚 students recycle.
(b) Suppose 63 students in the class鈥檚 sample say 鈥淵es.鈥� Explain why this result gives strong evidence that a majority of the school鈥檚 students recycle.
Keep on tossing The figure below shows the results of two different sets of coin tosses. Explain what this graph says about chance behavior in the short run and the long run.
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