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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.
 Spring '11
 dat

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