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STAT 200 Week 3 Homework Complete Solution
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Week 3

Instructions    

Week   #          Text                 Chapter            Exercise          page

3          1          Lane et al.                   5                      7          217

3          2          Lane et al.                   5                      25        221

3          3          Lane et al.                   5                      27        222

3          4          Illowsky et al.             3                      86        207

3          5          Illowsky et al.             3                      98        209

3          6          Illowsky et al.             3                      112      210

3          7          Illowsky et al.             3                      124      214

3          8          Illowsky et al.             4                      72        268

3          9          Illowsky et al.             4                      80        270

3          10        Illowsky et al.             4                      88        271

 

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 their attractiveness. It should be clear that the format with the highest probability to pass is the most attractive format. Which would you choose and why?

 

 

Rank

Exam Format

Probability

1

II

= 0.0067

2

I

 = 0.0046

3

III

 = 0.0037

 

 

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