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mt1sol1 - York University MATH 2030 3.0AF(Elementary...

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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 letter-sized two-sided 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 0 ) ( 35 4 ) = ( 15 3 )( 20 1 ) ( 15 3 )( 20 1 ) + ( 15 4 )( 20 0 ) = 9100 10465 = 20 23 0 . 8696 2. [20] A, B, C are independent events, and P ( A ) = 0 . 6, P ( B ) = 0 . 7, P ( C ) = 0 . 8; Let D
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