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Unformatted text preview: Math 105 Prelim #2 October 28, 2004 This exam has a formula sheet, 7 problems and 7 numbered pages . You have 90 minutes to complete this exam. Please read all instructions carefully, and check your answers. Show all work neatly and in order, and clearly indicate your final answers. Answers must be justified whenever possible in order to earn full credit. Unless otherwise specified, no credit will be given for unsupported answers, even if your final answer is correct. Points will be deducted for incoherent, incorrect, and/or irrelevant statements. Calculators are permitted, but no other aids are allowed. You must answer all of the questions in the space provided. Note that blank space is NOT an indication of a questions difficulty. Name: Instructor: Problem Score 1 2 3 4 5 6 7 TOTAL: Formula Sheet Definition P ( E ) = n( E ) n( S ) , only for equally likely outcomes. Union P ( E F ) = P ( E ) + P ( F )- P ( E F ) Complement 1 = P ( E ) + P ( E ) Mutually Exclusive Events P ( E F ) = P ( E ) + P ( F ) Conditional Probability P ( E | F ) = P ( E F ) P ( F ) = n( E F ) n( F ) Independent Events P ( E F ) = P ( E ) P ( F ) , or P ( E | F ) = P ( E ) , or P ( F | E ) = P ( F ) Bayes Theorem P ( F i | E ) = P ( F i ) F ( E | F i ) P ( F 1 ) F ( E | F 1 ) + P ( F 2 ) F ( E | F 2 ) + + P ( F n ) F ( E | F n ) Bayes Theorem (Special Case) P ( F | E...
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- Fall '07