1
Assignment 1, STAT220Fall 2010
Instructor: Kamyar Moshksar
Due on September 20th
Problem 1
 Fig. 1 demonstrates the blocks in the downtown of a city. There are a total of 60 blocks.
A cab driver starts at point A and is called to go to point B. What is the probability that it passes by
intersection
C
shown in the figure. It is assumed that the cab driver only goes towards north or east at
each intersection with a probability of
0
.
5
each.
B
NORTH
EAST
WEST
SOUTH
C
A
Fig. 1.
Solution: In order to go from A to B, the cab driver must take
6
steps towards east (E) and
10
steps
towards north (N). Therefore, the number of ways he can do the trip is the same thing as arranging
6
letters
E
and
10
letters
N
on a line which is
16!
6!10!
. By the same token, there are
4!
1!3!
ways to travel from
A to C and
12!
5!7!
ways to travel from C to B. Hence, the answer is
4!
1!3!
12!
5!7!
16!
6!10!
.
Problem 2
A box contains
n
balls numbered
1
through
n
. Suppose
k
balls are drawn in succession.
(a)What is the probability that
m
is the largest number drawn? (b) what is the probability that the largest
number drawn is less than or equal to
m
?
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Burbidge,John
 Probability, Grammatical number, cab driver

Click to edit the document details