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 Distributions
Week 3
7. 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 only one of your flips?
The cases favorable to the event E1 of getting heads on only one of your flips are,
E1 = {(HTT), (TTH), (THT)}
n (E1) = 3
P (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 event E2 of getting heads on only one of your flips are,
E2 = {(HHH), (HHT), (HTH), (THH), (HTT), (TTH), (THT)}
n (E2) = 7
P (E2) = n (E2) / n (S) = 7/8 = 0.875
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
Events, and Distributions
Week 3
7. 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 only one of your flips?
The cases favorable to the event E1 of getting heads on only one of your flips are,
E1 = {(HTT), (TTH), (THT)}
n (E1) = 3
P (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 event E2 of getting heads on only one of your flips are,
E2 = {(HHH), (HHT), (HTH), (THH), (HTT), (TTH), (THT)}
n (E2) = 7
P (E2) = n (E2) / n (S) = 7/8 = 0.875
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
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