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mt1sol - York University MATH 2030 3.0AF(Elementary...

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York University MATH 2030 3.0AF (Elementary Probability) Midterm I - SOLUTIONS October 12, 2007 NAME: STUDENT NUMBER: You have 50 minutes to complete the examination. There are 5 questions on 4 pages. 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 solutions to the extent possible. You may leave numerical answers or binomial coefficient unsimplified, unless specifically told otherwise. Use the back of your page if you run out of room. 1. [10] P ( A ) = 0 . 3 and P ( B ) = 0 . 2; What value of P ( A B ) ensures that (a) A and B are independent? (b) A and B are disjoint? Solution: (a) If A and B are independent then P ( A B ) = P ( A ) + P ( B ) - P ( A B ) = P ( A ) + P ( B ) - P ( A ) P ( B ) = 0 . 3 + 0 . 2 - 0 . 3 × 0 . 2 = 0 . 44 (b) If A and B are disjoint then P ( A B ) = P ( A ) + P ( B ) = 0 . 3 + 0 . 2 = 0 . 5 2. [10] Suppose P ( A ) = 0 . 4, P ( B ) = 0 . 2, and P ( A | B ) = 0 . 7 Find P ( A B c ). Solution: P ( A B c ) = P ( A ) - P ( A B ) = P ( A ) - P ( B ) P ( A | B ) = 0 . 4 - 0 . 2 × 0 . 7 = 0 . 26 3. You are dealt 10 cards from a regular deck of 52 cards.
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