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Midterm_practice_sp07-1

# Midterm_practice_sp07-1 - of Aces dealt 4 In how many ways...

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Name: Student ID: CSE 21 Practice Midterm #1 Each problem is worth 20 points. Show your work to the extent you think it is necessary. Additional scratch paper is available at the front of the room. This is a CLOSED BOOK, NO CALCULATOR test. However, you may have one 8 1 / 2 by 11 inch sheet of paper with hand-written notes on it, if you wish. Answers can be left in unexpanded form, i.e., using ! and ( x y ) . Good luck! 1

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1. What is the probability that a random function from { A,B,C,D,E } to { 1,2,3,4 } is onto ? 2. An urn contains 2 red balls, 3 white balls and 4 blue balls. You reach into the urn and randomly remove three balls form the urn (without replacement). What is the probability that the balls removed all have different colors? (a) 1 7 (b) 2 7 (c) 1 2 (d) 3 7 (e) none of the above. 3. 4 cards are dealt from a randomly shuffled deck of 52 cards. What is the expected number
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Unformatted text preview: of Aces dealt? 4. In how many ways can 20 cookies and 30 jellybeans be distributed to 4 boys and 5 girls if every boy gets at least 2 cookies, and every girl gets at least 1 cookie and at least 3 jellybeans? 5. Seven light bulbs are selected at random from a set of 20 light bulbs of which 4 are defective. What is the probability that exactly two of the selected bulbs are defective? 6. Let A = (12345) and B = (13)(254) be two permutations on [5] = { 1 , 2 , 3 , 4 , 5 } . Which composition is equal to (1543)(2)? (a) A ◦ B ; (b) B ◦ A ; (c) B ◦ A ◦ B ; (d) A ◦ B ◦ A ; (e) none of the above. Note: X ◦ Y means that you apply Y ﬁrst, and then X . 2...
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