# Counting And Probability

### Farah Salem

## Probability Introduction

## Rules for Counting

There are two basic rules for counting which can deal with most problems. We phrase the rules in terms of ``jobs" which are to be done.

The **Addition Rule:**

Suppose we can do job 1 in P ways and job 2 in Q ways. Then we can do either job 1 or job 2, but not both, in P+Q ways.

1. For example, suppose a class has 30 men and 25 women. There are 30+25=55 ways the professor can pick one student to answer a question.

The **Multiplication Rule:**

Suppose we can do job 1 in P ways and an unrelated job 2 in Q ways. Then we can do both job 1 and job 2 in PxQ ways.

2. For example, to ride a bike, you must have the chain on both a front sprocket and a rear sprocket. For a 21 speed bike there are 3 ways to select the front sprocket and 7 ways to select the rear sprocket.

## For more information

There are many sites that you can go to and read about this subject, but I suggest the best site and the clearest:

http://www.intmath.com/counting-probability/counting-probability-intro.php