IE 255 Problem Set 3

IE 255 Problem Set 3 - many freshman girls must be present if sex and class are to be independent when a student is selected at random 4 Suppose

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Bogazici University Department of Industrial Engineering Fall 07, Probability for IE, IE 255 Problem Set #3 1) An ordinary deck of 52 playing cards is randomly divided into 4 piles of 13 cards each. What is the probability that each pile has exactly 1 ace? 2) English and American spellings are colour and color , respectively. A man staying at an Asian hotel writes this word, and a letter taken at random from his spelling is found to be a vowel. If 40 percent of the English speaking men at the hotel are English and 60 percent are Americans, a. what is the probability that the writer is an Englishman? b. this man writes another word behaviour or behavior and a letter is randomly chosen from this writing. What are the probabilities of choosing letters u and o ? 3) In a class there are there are 6 freshman boys, 9 sophomore boys and 18 sophomore girls. How
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Unformatted text preview: many freshman girls must be present if sex and class are to be independent when a student is selected at random? 4) Suppose that you continually collect coupons and that there are m different types. Suppose also that each time a new coupon is obtained it is a type i coupon with probability p i , i= 1, … ,m . Suppose that you have just collected your n th coupon. What is the probability that it is a new type? 5) Independent trials that result in a success with probability p and a failure with probability 1-p are called Bernoulli trials. Let P n denote the probability that n Bernoulli trials result in an even number of successes( 0 is considered as an even number) a. Show that P n = p(1- P n-1 ) + (1-p) P n-1 n ≥ 1 b. Use part a) to prove that P n =[1+ (1-2p) n ]/2...
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This homework help was uploaded on 04/19/2008 for the course IE 255 taught by Professor Aybekkorugan during the Fall '07 term at Boğaziçi University.

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