Midterm

# Midterm - that the balls removed all have diﬀerent...

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Name: Student ID: CSE 21 Midterm May 10, 2007 Each problem is worth 20 points. Show your work to the extent you think it is necessary (otherwise, it won’t be possible to get partial credit). Additional scratch paper is available at the front of the room. This is a CLOSED BOOK test. However, you may have one 8 1 / 2 by 11 inch sheet of paper with hand-written notes on it, if you wish. Calculators are allowed but won’t be necessary. Answers can be left in unexpanded form, i.e., using ! and ( x y ) . Good luck! Prob. Score 1 2 3 4 5 Total 1

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1. Let A = (12)(345) and B = (13)(245) by two permutations on [5] = { 1 , 2 , 3 , 4 , 5 } . Which composition is equal to (1524)(3)? (a) A B B ; (b) B A A ; (c) A B A ; (d) B A B ; (e) none of the above. 2. An urn contains 3 red balls, 4 white balls and 5 blue balls. You reach into the urn and randomly remove three balls from the urn (without replacement). What is the probability
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Unformatted text preview: that the balls removed all have diﬀerent colors? (a) 1 4 ; (b) 2 7 ; (c) 3 11 ; (d) 4 13 ; (e) none of the above. 3. 2 cards are selected at random from an ordinary deck of 52 cards. Let X denote the number of Aces selected and let Y denote the number of Hearts selected. What is the expected value of X + Y ? 4. In how many ways can 20 cookies and 25 jellybeans be distributed to 3 boys and 4 girls if every boy gets at least 2 cookies, and every girl gets at least 1 cookie and at least 2 jellybeans? 5. Six light bulbs are selected at random from a set of 20 light bulbs of which 5 are defective. What is the probability that exactly two of the selected bulbs are defective? 2...
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## This note was uploaded on 12/03/2009 for the course CSE 21 taught by Professor Graham during the Spring '07 term at UCSD.

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Midterm - that the balls removed all have diﬀerent...

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