help for 9,11,13 3.4 Multiplication Rule: Basics with the random selection of tw
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help for 9,11,13
3.4 Multiplication Rule: Basics with the random selection of two gas masks from this population, find the probability that they are both defective. a. Assume that the first gas mask is replaced before the next one is selectecd. b. Assume that the first gas mask is not replaced before the second item is selected. c. Compare the results from parts (a) and (b). d. Given a choice between selecting with replacement and selecting without replace- ment, which choice makes more sense in this situation? Why? 8. Wearing Hunter Orange A study of hunting injuries and the wearing of "hunter" or- ange clothing showed that among 123 hunters injured when mistaken for game, 6 were wearing orange (based on data from the Centers for Disease Control). If a fol- low-up study begins with the random selection of hunters from this sample of 123, find the probability that the first two selected hunters were both wearing orange. a. Assume that the first hunter is replaced before the next one is selected. b. Assume that the first hunter is not replaced before the second hunter is selected. c. Given a choice between selecting with replacement and selecting without replace- ment, which choice makes more sense in this situation? Why? 9. Probability and Guessing A psychology professor gives a surprise quiz consisting of 10 true/false questions, and she states that passing requires at least 7 correct re- sponses. Assume that an unprepared student adopts the questionable strategy of guessing for each answer. a. Find the probability that the first 7 responses are correct and the last 3 are wrong. b. Is the probability from part (a) equal to the probability of passing? Why or why not? 10. Selecting U.S. Senators In the 107th Congress, the Senate consists of 13 women and 87 men. If a lobbyist for the tobacco industry randomly selects three different sena- tors, what is the probability that they are all women? Would a lobbyist be likely to use random selection in this situation? I1. Coincidental Birthdays a. The author was born on November 27. What is the probability that two other ran- domly selected people are both born on November 27? (Ignore leap years.) b. What is the probability that two randomly selected people have the same birthday? Ignore leap years.) 12. Coincidental Birthdays a. One couple attracted media attention when their three children, born in different years, were all born on July 4. Ignoring leap years, find the probability that three randomly selected people were all born on July 4. Is the probability low enough so that such an event is not likely to occur somewhere in the United States over the course of several years? b. Ignoring leap years, find the probability that three randomly selected people all have the same birthday 13. Acceptance Sampling With one method of a procedure called acceptance sam- pling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. The Niko Electronics Com- pany has just manufactured 5000 CDs, and 3% are defective. If 12 of these CDs are randomly selected for testing. what is the probability that the entire batch will be accepted?Explanation / Answer
9.
a. Assuming, the student is randomly guessing T/F, each with equal probability. Then, the probability that the student gets a particular question correct is 0.5, independent of other questions.
Therefore, Prob(1st seven are correct and last 3 are wrong) = P(1st seven are corect) * P(last 3 are wrong)
= P(1st question is correct) * P(2nd questioon is correct) * ........ * P(7th question is correct) * P(8th question is wrong) * P(9th question is wrong) * P(10th question is wrong)
= 0.57 * (1-0.5)3 = 0.57 * 0.53 = 0.510
b.
Getting 1st seven correct and last 3 wrong is one way to pass. There are several other ways to get at least 7 correct and pass, for example, getting 1st three wrng and rest seven correct. A student can pass in any of those ways. So, the probability of passing will be the sum of the probabilities of all such events that lead to passing. Therefore, the probability of passing is much higher than the probability of the event in part (a).
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