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Probability and Statistics: College Assignment on Random Experiments, Events, and Distributions

Assignment on probability theory, event distributions, and statistical applications.

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Probability and Statistics: College Assignment on Random Experiments,Events, and DistributionsWeek 37.You flip a coin three times.The possible outcomes of this random experiment are,S ={(HHH), (HHT), (HTH), (THH), (HTT), (TTH), (THT),(TTT)}n (S) = 8(a) What is the probability of getting heads on onlyone of your flips?The cases favorable to the eventE1of gettingheads on only one of your flipsare,E1={(HTT), (TTH), (THT)}n (E1) = 3P (E1) = n (E1) / n (S) = 3/8 =0.375(b) What is the probability of getting heads on at least one flip?The cases favorable to the eventE2of gettingheads on only one of your flipsare,E2={(HHH), (HHT), (HTH), (THH), (HTT), (TTH), (THT)}n (E2) = 7P (E2) = n (E2) / n (S) =7/8 = 0.87525.You are to participate in an exam for which you had no chance to study, and for that reasoncannot 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 ofoptions (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. 6questions of the 4-choice type; you pass when 5 or more answers are correct; II. 5 questions ofthe 5-choice type; you pass when 4 or more answers are correct; III. 4 questions of the 10-choicetype; you pass when 3 or more answers are correct. Rank the three exam formats according to

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