# Counting And Probability

## Probability Introduction

Probability is a measure or estimation of how likely it is that something will happen or that a statement is true. Probabilities are given a value between 0 (0% chance or will not happen) and 100 (100% chance or will happen). The higher the degree of probability, the more likely the event is to happen.

## 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.

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.

10.3 Counting Methods and Probability (Lesson)