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
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?
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.
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
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?
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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Document Details
University
University of Maryland
Subject
Statistics