2901hw1.pdf

# 2901hw1.pdf - THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

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P. 1 THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT2901 PROBABILITY AND STATISTICS: FOUNDATIONS OF ACTUARIAL SCIENCE Assignment 1 Due Date: February 12, 2018 (Hand in your solutions for Questions 53 - 63) 1. A total of 7 different gifts are to be distributed among 13 children. How many distinct results are possible if no child is to receive more than one gift? 2. From a group of 8 women and 6 men a committee consisting of 4 men and 4 women is to be formed. How many different committees are possible if (a) 2 of the men refuse to serve together; (b) 2 of the women refuse to serve together; (c) 1 man and 1 woman refuse to serve together? 3. In how many ways can 12 people be seated in a row if (a) there are no restrictions on the seating arrangement; (b) persons A and B must sit next to each other; (c) there are 6 men and 6 women and no 2 men or 2 women can sit next to each other; (d) there are 5 men and they must sit next to each other; (e) there are 6 married couples and each couple must sit together? 4. Four separate awards (best scholarship, best leadership qualities, and so on) are to be presented to selected students from a class of 25. How many different outcomes are possible if (a) a student can receive any number of awards; (b) each student can receive at most 1 award? 5. ( Poker ) If it is assumed that all 5 52 poker hands are equally likely, what is the probability of being dealt (a) one pair? (This occurs when the cards have denominations a, a, b, c, d where a, b, c, and d are all distinct.) (b) two pairs? (This occurs when the cards have denominations a, a, b, b, c , where a, b, and c are all distinct.) (c) three of a kind? (This occurs when the cards have denominations a, a, a, b, c .) (d) a straight? (Five consecutive cards of any suits which are not all the same, including 10, J, Q, K, A .) (e) a flush? (Five cards of the same suit and not all in consecutive order.) (f) full house? (This occurs when the cards have denominations a, a, a, b, b .) (g) four of a kind? (This occurs when the cards have denominations a, a, a, a, b .) (h) a straight-flush? (Five consecutive cards of the same suit, including 10, J, Q, K, A .)

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