Economics 404 Winter 2014 -Midterm I

Version 1
Midterm I Solutions
Economics 404 Winter 2014
University of Michigan

Each question is worth 5 points. The answers of these questions should go on the scantron sheet.
1. If two events with positive probabilities are mutually exclusive, they cannot be independent.
(a) True
(b) False

2. If Samantha has _ve blue socks and four green ones in her sock drawer, what is the probability that a randomly chosen group of three contains exactly two blue socks?
(a) 0.476
(b) 0.498
(c) 0.255
(d) 0.444
(e) None of the above.

3. If a basketball player misses free throws 10% of the time and this probability is constant every time he shoots, the probability that he will miss at least one of the next 3 shots is:
(a) 0.729
(b) 0.810
(c) 0.370
(d) 0.271
(e) Not enough information to answer the question.

4. Events A and B are independent and probability of A is 0.5. If the probability of the union of A and B is 0:9, what is the probability of event B?
(a) 0.5
(b) 0.8
(c) 0.7
(d) 0.6
(e) None of the above

5. Salma generated a 4 digit PIN code for her ATM card when she _rst got it. Ten years later, she realized that she still had a few bucks in that account and decided withdraw them. But she forgot the code besides the _rst and last digits. She remembers that it was 8??9. If numbers can take any value
between 0-9, but they cannot be repeated; what is the probability that she will guess the right code in her _rst attempt at the ATM machine?
(a) 1=90
(b) 1=56
(c) 1=45
(d) 1=72
(e) The probability is zero, she’d better call the number on the card.

6. Consider a random experiment of rolling 3 dice in a row (a six-sided fair one). Suppose that we are interested in the sum of the face values showing on the dice. What is the probability that this sum will be larger than or equal to 5?
(a) 15/108
(b) 212/216
(c) 105/108
(d) 180/126
(e) None of the above.

7. Turkish Lira (currency of Turkey) had a terrible last week. On Monday, it depreciated 4% against the dollar, on Tuesday depreciated 5%, on Wednesday depreciated 3%, and on Thurday it again depreciated 6%. Turkish Central Bank increased the interest rate Thursday night and was able to appreciate the currency 2% on Friday. What was the daily geometric average return (or loss) rate of Lira over last
(Hint: You can think about the value of a foreign currency as a regular asset for the purposes of this question (like a stock). Depreciation means loss of value. Appreciation is the opposite.)
(a) 0.0310
(b) -0.0216
(c) -0.0248
(d) -0.0324
(e) None of the above

8. A health survey done by UHS asks students several questions:
(i) What is your gender? \Male” or \Female”
(ii) What is your current weight?
(iii) What is your degree of satisfaction with your weight? Choose between
\Not happy with it”, \Somewhat happy with it”, \Happy with it” What types of measurement scale do the answers to these questions have? (in the order i,ii,iii )
(a) Ratio, Nominal, Ordinal
(b) Ordinal, Ordinal, Nominal
(c) Nominal, Ratio, Ordinal
(d) Nominal, Interval, Ordinal
(e) Nominal, Interval, Nominal

9. Suppose Econ 404 has two sections. Both sections have the same number of students. In section I, 15 percent of the students are female. In section II, 45 percent of students are female. What is the probability that a randomly selected student from Econ 404 class is in Section II given that he is male?
(a) 0.555
(b) 0.432
(c) 0.52
(d) 0.054
(e) 0.393

10. Yulia needs to take a trip tomorrow. She generally doesn’t like to travel. If the weather is not good, she hates it even more. Her utility from the trip depends on the weather, which is unknown the day  before. Her level of utility from the trip is a function of temperature during the trip (T), and is
in this form:

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