ISyE 2027 Probability with Applications Fall 2006 R. D. Foley Homework 2 August 30, 2006 due on Tuesday, 5 September 1. (a) If we toss a coin once and then roll a die once, what would be a reasonable sample space S ? (b) How many outcomes are in your sample space? (c) If we assume the die and coin are fair, are the outcomes equally likely? 2. Suppose we have a sample space with Pr( A ) = . 4, Pr( B ) = . 3, and Pr( A ∩ B ) = . 1. Compute (a) Pr( ¯ A ), where ¯ A denotes the complement of A , (b) Pr( A ∪ B ), (c) Pr( ¯ A ∩ ¯ B ), and (d) Pr( ¯ A ∪ ¯ B ). (e) Are A and B disjoint? 3. (a) If Georgia license plates are 3 numbers followed by 3 letters, how many possible license plates are there? (b) How many of the license plates do not have any repeated digits or letters? 4. Compute ( 6 2 ) , ( 6 1 ) and ( 60 ) . 5. How many diﬀerent four person committees can be made from 10 diﬀerent people? How many diﬀerent sets of oﬃcers (president, vice president, treasurer, and secretary) can be selected from 10 people? 6. Suppose we randomly grab 3 balls without replacement from an urn con-
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