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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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Common names The Census Bureau says that the most common names in the United States are (in order) Smith, Johnson, Williams, Brown, Jones, Miller, Davis, Garcia, Rodriguez, and Wilson. These names account for of all U.S. residents. Out of curiosity, you look at the authors of the textbooks for your current courses. There are authors in all. Would you be surprised if none of the names of these authors were among the most common? (Assume that authors鈥� names are independent and follow the same probability distribution as the names of all residents.)
Color-blind men Refer to Exercise . Suppose we randomly select U.S. adult males. What鈥檚 the probability that at least one of them is red-green
color-blind? Design and carry out a simulation to answer this question. Follow the four-step process.
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.
Role-playing games Computer games in which the players take the roles of characters are very popular. They go back to earlier tabletop games such as Dungeons & Dragons. These games use many different types of dice. A four-sided die has faces with and spots.
(a) List the sample space for rolling the die twice (spots showing on first and second rolls).
(b) What is the assignment of probabilities to outcomes in this sample space? Assume that the die is perfectly balanced.
Medical risks Morris鈥檚 kidneys are failing, and he is awaiting a kidney transplant. His doctor gives him this information for patients in his condition: 90% survive the transplant and 10% die. The transplant succeeds in 60% of those who survive, and the other 40% must return to kidney dialysis. The proportions who survive five years are 70% for those with a new kidney and
50% for those who return to dialysis.
(a) Make a tree diagram to represent this setting.
(b) Find the probability that Morris will survive for five years. Show your work.
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