Question Version 1 Midterm I Solutions

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

I. MULTIPLE CHOICE QUESTIONS:
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.

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