Counting And Probability

Farah Salem

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.

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.

10.3 Counting Methods and Probability (Lesson)

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