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Unformatted text preview: 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? Answer: 210. 2. If n balls are randomly placed into n cells, what is the probability that each cell will be occupied. Answer: n ! n n . 3. An integer is selected at random from the set { 1 , 2 ,..., 100 , 000 } . What is the probability that it contains the digit 4? Answer: 1 9 5 10 5 ≈ . 41 . 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? Answer: 0.134. 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. Answer: 0.036. 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?...
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 Spring '08
 Feinberg,E
 Probability, Variance, Probability theory, probability density function

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