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Unformatted text preview: York University MATH 2030 3.0AF (Elementary Probability) Midterm Exam I SOLUTIONS October 17, 2008 NAME: STUDENT NUMBER: You have 50 minutes to complete the examination. There are 4 pages, containing 5 questions. You may bring one lettersized twosided formula sheet to the exam. No other books or notes may be used. You may use a calculator. Show all your work, and explain or justify your answers. You may leave numerical answers unsimplified, including binomial coefficients. Use the back of your page if you run out of room. 1. [20] An urn has 15 red balls and 20 yellow balls. You choose 4 balls at random, without replacement. Find P (at most 3 red balls are chosen  at least 3 red balls are chosen) Solution: P (at most 3 red  at least 3 red) = P (at most 3 red and at least 3 red) P (at least 3 red) = P (exactly 3 red) P (at least 3 red) = P (exactly 3 red) P (exactly 3 red) + P (exactly 4 red) = ( 15 3 )( 20 1 ) ( 35 4 ) ( 15 3 )( 20 1 ) ( 35 4 ) + ( 15 4 )( 20 ) ( 35 4 ) = ( 15 3 )( 20 1 ) ( 15 3...
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 Winter '09
 SIKH
 Probability

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