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# quiz1BS-M_f10 - Econ 506 Section M Quiz 1B Sept 16 2010...

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Econ 506, Section M NAME:_ SOLUTION_ _____ Quiz 1B, Sept., 16, 2010 Total points: 50 I. (10 points) A and B play tennis and P (A wins) = 0.3. Suppose that A and B play two matches. What is the probability that A wins at least one match? Let AB denotes the event that player A wins the first match and player B wins the second. The sample space is S = {AA, AB, BA, BB}. Now the P ( A wins at least one match) = P({AA, AB, BA}) = P({AA}) + P({AB}) + P({BA}) = 0.09 + 0.21 + 0.21 = 0.51 II. (5 points) If A and B are mutually exclusive events and P (B) > 0, show that ) ( ) ( ) ( ) | ( B P A P A P B A A P + = . III. A delegation of three is to be chosen from the untenured faculty of the UIUC Economics Department (numbering 8) to represent the department in an Institute-wide committee. a) (5 points) in how many ways can the delegation be chosen? 56 3 8 = = r n b) (5 points) in how many ways can the delegation be chosen if two people refuse to go together? We compute 56 -#(Both are chosen to go together). There is only one way to choose both of them in a combination sense. This leaves us with 6 different ways to pick the

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quiz1BS-M_f10 - Econ 506 Section M Quiz 1B Sept 16 2010...

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