The document contains several math and probability word problems and examples presented as homework assignments. It provides the questions, working, and answers for problems involving Pascal's triangle, counting paths, probability, coin flipping, and spinners. The document is a collection of homework questions and solutions on topics of combinatorics, probability, and experimental vs theoretical probability.

1. February 25, 2009
Zhu Shijiei 1261
Pascal 1653

2. February 25, 2009
Find a pattern, add two more rows to the triangle ...
1
1
1 1
1 1
1 2 1
1 2 1
1 3 3 1
1 3 3 1
1 4 6 4 1
1 4 6 4 1

3. February 25, 2009
Pascal's Triangle
How many different patterns can you find in the triangle?

4. February 25, 2009
Suppose that, when you go to school from home, you like to take as great a
variety of routes as possible, and that you are equally likely to take any
possible route. You will walk only east or south.
(a) How many ways can you go to the
post office?
(b) How many ways can you go to
school?
(c) What is the probability that you will walk past the post office on your
way to school?

5. February 25, 2009
There are 3 ways to get to the post office. For each of those 3
ways, there are 4 ways to get to school - so altogether, there
are 12 ways to get from home to school past the post office.

6. February 25, 2009
How many ways can the word RIVER be found in the array of letters shown to the
right if you start from the top R and move diagonally down to the bottom R?

7. February 25, 2009
HOMEWORK
A water main broke in our
neighborhood today. My kids
want to get to the park to play as
quickly as they can so we only
walk South or East. How many
different quot;shortest pathsquot; are there
from our house to the park
walking on the sidewalks along
the streets?

8. February 25, 2009
HOMEWORK How many ways can the word
quot;MATHEMATICSquot; appear in the
following array if you must spell
the word in proper order?

9. February 25, 2009
HOMEWORK
The diagram below shows a game of chance where a ball is dropped as indicated,
and eventually comes to rest in one of the four locations labelled A, B, C, or D.
The ball is equally likely to go left or right each time it strikes a triangle. We
want to determine the theoretical probability of a ball landing in any one of these
four locations. To do this, we need to know the total number of paths the ball can
take, and also the number of paths to each location.

10. February 25, 2009
As your birthday approaches you are looking for
ways to make money so you can buy a used car. Currently,
you earn $10 a week for doing chores around the house.
Your parents realize that you are trying to save up,
and offer you the following deal. You can either be paid the
$10, or you can pull two bills from a brown paper bag. In the
bag there are two $1 bills, two $5 bills, and a $10 bill. For
example, you might pull out a $1 bill followed by a $5 bill, and
earn only $6. Or you might pull out the $10 bill followed by a $5
bill and earn $15.
If you were given this option every week, what would be
better for you to do in the long run? Is pulling two bills from the
paper bag a great way to make money? Be sure to give a
complete explanation of how you found your answer.

11. February 25, 2009
HOMEWORK
What is the probability of spinning each of the following using the
spinner shown? The colours on the spinner are red, yellow, and blue.
1. P(red)
2. P(yellow)
3. P(green)
4. P(red, yellow or blue)
5. P(not red)

12. February 25, 2009
HOMEWORK
Design an experiment using coins to simulate a 10 question true/false test.
What is the experimental probability of scoring at least 70% on the test if
you guess each answer?

13. February 25, 2009
HOMEWORK
Design an experiment to determine the probability of passing a six-question
multiple choice test if you guess all the answers. Each question has four
answers, and one answer is correct in each case.
How many simulations would seem reasonable?
What is the experimental probability of getting at least 50% on the test?