sheets - Exercises to Accompany"Statistics for Management...

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Exercises to Accompany “Statistics for Management and Economics,” by Watson et al written (except where indicated) and compiled by Cymra Haskell Please note: These exercises are meant to supplement rather than replace the exercises in the text.
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Sheet I Probability 1. Consider the experiment of choosing one person at random from all students at USC. Consider the events: A = the student is female B = the student is a junior C = the student is a senior D = the student has taken a math course E = the student is in the business school Describe the following events in words. (a) A c (b) B C (c) ( B C ) c (d) B C (e) A E (f) C D c 2. Consider the experiment of drawing two cards from a deck of cards. Consider the events: A = 1st card is a face card B = 1st card is an ace C = 2nd card is a face card D = 2nd card is an ace In parts (a)-(f) write the event described in terms of A , B , C , and D . (a) Both cards are aces. (b) Neither card is an ace. (c) Exactly one of the cards is an ace. (d) The 1st card is either a face card or an ace. (e) At least one of the cards is a face card. (f) The 1st card is neither a face card nor is it an ace. (g) Consider all the pairs of events: AB , AC , AD , BC , BD , CD . Which of them, if any, are mutually exclusive? 3. For each experiment either draw a picture of the sample space that clearly indicates all its mem- bers, or list every element in the sample space, or describe clearly what the elements of the sam- ple space are in such a way that it is apparent how many elements there are total. In each case choose the sample space so that all the outcomes are equally likely. 4. Consider the experiment of rolling a pair of dice. (a) Are the events “sum is 6” and “at least one of the dice shows a 3” mutually exclusive? (b) Are the events “sum is 6” and “at least one of the dice shows a 6” mutually exclusive? (c) Are the events “at least one of the dice shows a 3” and “at least one of the dice shows a 6” mutually exclusive?
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