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Unformatted text preview: MATH/STAT 418 Section 002 2008/06/26 Exam 1 Sample Instructions: 1. There are six problems in this exam. The entire exam is worth 100 points and the point distribution is noted next to each problem. 2. Please show all work as detailed as possible in order to receive full credit. 3. The exam is closed book and closed notes, but you may have one doublesided 8.5" x 11"formula sheet, and you are allowed to use calculator. 4. The exam is 75 minutes. Name:  PSU ID:  1. (15 points) Consider the grid of points shown below. Suppose that the starting point is labeled A, you can go one step up or one step to the right at each move. This is continued until the point labeled B is reached. (a) How many different paths from A to B are possible? (b) If you are required to pass two points, C and D, in your journey, how many different paths from A to B are possible? 2. (15 points) Consider the expansion of (x + 2 y + z ) . How many different terms 4 are there in the expansion? What is the coefficient of the term xy 2 z ? 3. (20 points) Suppose that 60% of students are men; 40% of the students wear blue jeans. 20% of the students are women and do not wear jeans. What is the percentage of students who are men and wear jeans? 4. (20 points) Let A denote the event that the midtown temperature in Los Angeles is 70oF, and let B denote the event that the midtown temperature in New York is 70oF. Also, let C denote the event that the maximum of the midtown temperature in New York and in Los Angeles is 70oF. IF P(A) = 0.3, P(B)=0.4, P(C)=0.2, find the probability that the minimum of the two midtown temperatures is 70oF. 5. (15 points) A president, treasure, and secretary, all different, are to be chosen from a club consisting of 10 people. How many different choices of officers are possible if (i) there are no restrictions; (ii) A and B will not serve together? 6. (15 points)There are 25 statisticians and 25 mathematicians attending a certain conference. Four of these 50 people are randomly chosen to take part in a panel discussion. What is the probability that at least one statistician is chosen? ...
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This note was uploaded on 06/28/2008 for the course MATH 418 taught by Professor Arnold,stevenfdong,yuexiao during the Summer '08 term at Pennsylvania State University, University Park.
 Summer '08
 ARNOLD,STEVENFDONG,YUEXIAO
 Math, Probability

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