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samplefinal

# samplefinal - AMS507 Introduction to Probability Sample...

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AMS507 Introduction to Probability. Sample Final Test Fall, 2009 You shall receive 5 points for each of the following 20 questions. 1. In how many ways can a man divide 7 gifts among his 3 children if the eldest is to receive 3 gifts and the others 2 each? 2. If n balls are randomly placed into n cells, what is the probability that each cell will be occupied. 3. An integer is selected at random from the set { 1 , 2 , . . . , 100 , 000 } . What is the probability that it contains the digit 4? 4. A number is selected randomly from the set { 1 , 2 , . . . , 1000 } . What is the probability that it is divisible by 5 but not by 3? 5. From a group of 3 freshmen, 4 sophomores, 4 juniors, and 3 seniors a committee of size 4 is randomly selected. Find the probability that the committee will consist of 2 sophomores and 2 juniors. 6. A number is selected at random from the set of natural numbers { 1 , 2 , . . . , 1000 } . What is the probability that it is not divisible by 5, 7, or 8? 7. You asked your neighbor to water a plant while you are on vacation.

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samplefinal - AMS507 Introduction to Probability Sample...

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