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### assignment 3

Course: ECON 249, Spring 2008
School: Holy Cross (MA)
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249 Economics Assignment 3 Due Friday, February 8th R. Baumann Directions: Answer all questions on a separate piece of paper. Please do not turn in the questions. Be sure to use full sentences and show your work where applicable. 1. For the random experiment of rolling two dice, recall the sample space is S {(1,1), (1,2),..., (1,6), (2,1),..., (2,6), (3,1),..., (3,6), (4,1),..., (4,6),..., (5,1),..., (5,6),...

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249 Economics Assignment 3 Due Friday, February 8th R. Baumann Directions: Answer all questions on a separate piece of paper. Please do not turn in the questions. Be sure to use full sentences and show your work where applicable. 1. For the random experiment of rolling two dice, recall the sample space is S {(1,1), (1,2),..., (1,6), (2,1),..., (2,6), (3,1),..., (3,6), (4,1),..., (4,6),..., (5,1),..., (5,6), (6,1),..., (6,6)} Or, S {Oij (i, j ); i, j 1,2,..., 6} . a) What is the probability of rolling a pair, i.e. when both dice are the same number? b) What is the probability the sum of the dice will be seven or eleven? c) What is the probability the sum of the dice will be ten or rolling a pair? 2. For houses on the real estate market, 20% have a pool and 50% have a garage. In addition, 15% of houses with a pool do not have a garage. a) Define the events and write the probabilities given in the setup. b) What is the probability that a house has a pool a and garage? c) What is the probability that a house has a pool or a garage? d) What is the probability that a house with a garage does not have a pool? e) Are having a pool and having a garage independent events? 3. Suppose a lock is opened with the correct sequence of three numbers between 1 and 10, inclusive. Assume the same number cannot be used more than once, and each number is independent from one another. a) Suppose you have three guesses. What is the probability you will open the lock? b) You are told that 3 and 7 are in the solution, but you are not given their position. What is the probability you will open the lock with one guess? (Hint: Let P = putting 3 and 7 in the right spot, T = matching the third number, and use the property of independence.) 4. Assume there are two events A and B in a sample space where Pr(A) 0 , and Pr(B) 0 . Is it possible for A and B to be mutually exclusive and statistically independent? Show your work.
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