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Assignment 1 - SMSL/07 THE UNIVERSITY OF HONG KONG...

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SMSL/07 THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1301 Probability and Statistics I Assignment 1 Section A 1. Out of 8 participants in a competition, 1 winner, 1 first runner-up and 1 second runner-up are to be selected. (a) Calculate the number of different ways to select the winner, first and second runners-up. (b) Calculate the number of different possible combinations of the 5 losers. 2. How many distinguishable outcomes can be generated by rolling six identical dice simultane- ously, (a) if the six faces of each die are numbered distinguishably? (b) if each die has two red faces and four blue faces so that faces of the same colour are indistinguishable? 3. A committee consisting of 1 president, 2 vice presidents, 2 secretaries and 10 general managers are to be selected from 20 people. How many arrangements are possible? 4. Specify the outcome spaces and the corresponding outcome probabilities for the following ex- periments: (a) a fair coin is tossed three times;
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