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**Date Submitted:** 09/27/2011 05:10 AM

ISOM 3540, Fall 2011

1

Homework 1 Due: Wednesday, Sep 28, 15:00pm

Submit to the “ISOM 3540 Homework Collection Box” outside Room 4351

Unless instructed otherwise, for all questions you should present the logic underlying your answer, in at least as much detail as the reference book by Ross gives for the answers to the self-test problems. This rule applies to all homework. 1. Problem 7, page 16 in Ross (i.e., the reference book “A First Course in Probability”, 8th Edition, by Sheldon Ross). 2. In (ﬁve-card draw) poker, you are dealt 5 cards. A poker hand with four cards of one rank and any other card is called a four of a kind. Find the probability of being dealt a four of a kind. 3. Find the probability of winning a 4th division prize in Hong Kong Mark Six (see Lecture 2 notes for the background information). 4. Four friends plan to celebrate the New Year together. For the New Year’s gifts, they decide that each of them shall bring a gift (so totally there will be 4 gifts), and then they will put the 4 gifts in 4 identical boxes, and then each of them randomly chooses one box as his/her New Year’s gift. What’s the probability that none of them gets his/her own prepared gift? 5 - 8. Problems 13 (c) (d) and (e), 35, 45, 56, pages 50 - 54 in Ross. 9 - 14. Problems 10, 14, 25, 32, 35, 50, pages 102 - 107 in Ross. 15. m balls are put in n bins randomly. (a) What is the chance that the 1st bin is empty? (b) What is the chance that there is at least one empty bin if m = n = 10?