1. The document describes several probability problems involving experiments with coins, multiple choice tests, and paths on grids. It asks the reader to determine probabilities of outcomes for these experiments, count total possible outcomes, and find patterns in Pascal's triangle. 2. It also includes word search problems finding paths to spell words in letter arrays and determining the number of possible "shortest paths" between two points on a street map. 3. The reader is asked to complete the Pascal's triangle, simulate experiments involving coins and tests, and calculate probabilities and counts of outcomes for the various spatial problems and games of chance described.

1. Zhu Shijiei 1261
Pascal 1653

2. 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)

3. 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?

4. 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?

5. Zhu Shijiei 1261
Pascal 1653

6. 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

7. Pascal's Triangle
How many different patterns can you find in the triangle?

8. 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?

9. 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?

10. 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?

11. 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.

12. HOMEWORK How many ways can the word
quot;MATHEMATICSquot; appear in the
following array if you must spell
the word in proper order?