230hw1 - October 3, 2011 MATH 230 Homework #1 (Due: October...

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October 3, 2011 MATH 230 Homework #1 (Due: October 10, Monday) ( Submit your homework to my office till 5:00 pm) (Please, DO NOT forget to write your section number to your homework) 1. There are k boxes. Balls are placed at random one at a time into the boxes until, for the first time, some box has two balls. Find the probability that this occurs with the n th ball. 2. Suppose n distinguishable balls are distributed at random into r boxes. Find the probability that there are exactly k balls in the first r 1 boxes. 3. Suppose we have a box containing N balls numbered 1, 2, …N. A random sample of size n is drawn without replacement and the numbers on the balls noted. These balls are than returned to the box and a second random sample of size m is then drawn without replacement. Find the probability that two samples had exactly k balls in common. 4. A bus starts with r people and stops at n different stops ( r < n ). Assuming that passengers are equally likely to depart at any stop, find the probability that
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This note was uploaded on 12/22/2011 for the course CS 101 taught by Professor Dat during the Spring '11 term at Bilkent University.

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