sheets - Exercises to Accompany Statistics for Management...

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Unformatted text preview: 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. 2 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. (a) Roll two dice. (b) Select an entree at random from the three fish, three meat, and four vegetarian entrees offered at a restaurant. (c) Select two marbles at random (without re- placement) from a bag that contains a red marble, an orange marble, a yellow marble, a green marble, and a blue marble. (d) Select two marbles at random (without re- placement) from a bag that contains one blue marble and three green marbles. (e) Two siblings, Aisha and Bob, are randomly assigned to the chores of cleaning the bath- room, washing the dishes, and mopping the floor in such a way that each chore gets done and each sibling could end up doing none of the chores, exactly one of the chores, two of the chores or all three of the chores. (f) Select three people at random (without re- placement) from Andrew, Betty, Chuck, David and Elizabeth. (g) Select three people at random (without re- placement) from a group of two girls and three boys. 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?...
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sheets - Exercises to Accompany Statistics for Management...

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