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STAT 200 Week 3 Homework Solution Correct Answers

Week 3 homework solutions covering statistical problem-solving techniques.

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    STAT 200 Week 3 Homework Solution Correct Answers 7. You flip a coin three times. (a) What is the probability of getting heads on only one of your flips? (b) What is the probability of getting heads on at least one flip? 25 . You are to participate in an exam for which you had no chance to study, and for that reason cannot do anything but guess for each question (all questions being of the multiple choice type, so the chance of guessing the correct answer for each question is 1/d, d being the number of options (distractors) per question; so in case of a 4 - choice question, your guess chance is 0.25). Your instructor offers you the opportunity to choose amongst the following exam formats: I. 6 questions of the 4 - choice type; you pass when 5 or more answers are correct; II. 5 questions of the 5 - choice type; you pass when 4 or more answers are correct; III. 4 questions of the 10 - choice type; you pass when 3 or more answers are correct. Rank the three exam formats according to their attractivene ss. It should be clear that the format with the highest probability to pass is the most attractive format. Which would you choose and why? 27 . A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11 plums, and 2 mangos. a. Imagine you stick your hand in this refrigerator and pull out a piece of fruit at random. What is the probability that you will pull out a pear? b. Imagine now that you put your hand in the refrigerator and pull out a piece of fruit. You decide you do not want to eat that fruit so you put it back into the refrigerator and pull out another piece of fruit. What is the probability that the first piece of fruit you pull out is a banana and the second piece you pull out is an apple? c. What is the probability that you stick your hand in the refrigerator one time and pull out a mango or an orange? 86. Roll two fair dice. Each die has six faces. a. List the sample space. b. Let A be the event that either a three or four is rolled first, followed by an even number. Find P ( A ). c. Let B be the event that the sum of the two rolls is at most seven. Find P ( B ). d. In words, explain what “ P ( A | B )” represents. Find P ( A | B ). e. Are A and B mutually exclusive events? Explain your answer in one to three complete sentences, including numerical justification.

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    f. Are A and B independent events? Explain your answer in one to three complete sentences, including numerical justification. 98. At a college, 72% of courses have final exams and 46% of courses require research papers. Suppose that 32% of courses have a research paper and a final exam. Let F be the event that a course has a final exam. Let R be the event that a course requires a research paper. a. Find the probability that a course has a final exam or a research project. b. Find the probability that a course has NEITHER of these two requirements. 112. Table 3.22 identifies a group of children by one of four hair colors, and by type of hair. Hair Type Brown Blonde Black Red Totals Wavy 20 15 3 43 Straight 80 15 12 Totals 20 215 a. Complete the table. b. What is the probability that a randomly selected child will have wavy hair? c. What is the probability that a randomly selected child will have either brown or blond hair? d. What is the probability that a randomly selected child will have wavy brown hair? e. What is the probability that a randomly selected child will have red hair, given that he or she has straight hair? f. If B is the event of a child having brown hair, find the probability of the complement of B . g. In words, what does the complement of B represent? 124. Suppose that 10,000 U.S. licensed drivers are randomly selected. a. How many would you expect to be male? b. Using the table or tree diagram, construct a contingency table of gender versus age group.

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