7 Questions with Solution of Probability and Statistics - Exam 1 | ECON 209, Exams of Probability and Statistics

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Vassar College Economics 209 Probability and Statistics

Exam # I Name___________________________ Fall 2002 October 2, 2002

There are seven questions. You must show your work for full credit.

a) Find

b) Find

c)

d) Find

e)

2. A bag contains 10 coins, eight of which are regular coins and two of which are two headed coins. A coin is selected at random and flipped twice.

a) If the coin comes up heads the first time what is the probability that it is one of the two headed coins.

Let T = two headed coin, R= regular coin, H1 = first flip a head, H2 = second flip a head.

b) If the coin comes up heads on the first flip what is the probability that it comes up heads on the second flip as well.

3. A and B are two mutually exclusive events. P(A) = 1/4 , P(B) = 1/3. a) Find

b) Find

4. On the average there are 360 hits per hour on a popular web site. The probability of a hit in any time period is independent of whether there was a hit in any other time period. a) What is the probability that in any given minute there are exactly two hits.

b) What is the probability that two minutes go by without a single hit.

5. Suppose that four persons are selected at random. What is the probability that at least two of them have birthdays which fall in the same month. ( You may assume that the probability that a person is born in any month is equal to the probability that person is born in any other month.) P(at least two coincident birthdays) = 1-P(birthdays all different) = 1-(11/12)(10/12)(9/12) =.
6. A salesman makes ten calls a day. The probability that he makes a sale on any call is 0.4. Success on any call is independent of success on any of the other calls.

a) What is the probability that he makes two sales in a given day.

b) What is the probability that he makes at least two sales in a given day.

7. A manufacturer of light bulbs produces bulbs with a life span that is normally distributed with mean hours and standard deviation 150 hours. It is claimed in advertising that the bulbs last 2000 hours

a) What percentage of the bulbs last the advertised 2000 hours.

b) What should the standard deviation be reduced to if 99% of the bulbs are to last the advertised 2000 hours.