STAT 200 Week 3 HomeworkSolutionCorrect Answers7.You flip a coin three times. (a) What is the probability of getting heads on only one ofyour flips? (b) What is the probability of getting heads on at least one flip?25. You are toparticipate in an exam for which you had no chance to study, and for thatreason cannot do anything but guess for each question (all questions being of themultiple choice type, so the chance of guessing the correct answer for each question is1/d, d beingthe number of options (distractors) per question; so in case of a 4-choicequestion, your guess chance is 0.25). Your instructor offers you the opportunity tochoose amongst the following exam formats: I. 6 questions of the 4-choice type; youpass when 5or more answers are correct; II. 5 questions of the 5-choice type; you passwhen 4 or more answers are correct; III. 4 questions of the 10-choice type; you passwhen 3 or more answers are correct. Rank the three exam formats according to theirattractiveness. It should be clear that the format with the highest probability to pass isthe most attractive format. Which would you choose and why?27. A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11plums, 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 andpull out another piece of fruit. What is the probability that the first pieceof fruit you pullout 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 pullout a mango or an orange?86.Roll two fair dice. Each die has six faces.a.List the sample space.b.LetAbe the event that either a three or four is rolled first, followed by an evennumber. FindP(A).c.LetBbe the event that the sum of the two rolls is at most seven. FindP(B).d.In words, explain what “P(A|B)” represents. FindP(A|B).e.AreAandBmutually exclusive events? Explain your answer in one to three completesentences, including numerical justification.Preview Mode
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