Statistics

Statistics

Chapter 4: Basic Probability Theory

The probability is a measure that a given outcome will occur. Probability is measured from 0 to 1, with 0 indicating that an outcome will not occur and 1 indicating that an outcome will occur. Very rarely will you see a probability of 1. As statisticians, you will encounter values close to 1; the closer to 1, the more likely the outcome. This section will begin with a description of common terms followed by an in-depth explanation of the basic probability application. As we progress, do not forget to refer back to Chapters 1, 2, and 3.

Learning Objectives

After reading Chapter 4 and completing the workbook, you should be able to:

• Explain the definition of probability. • Explain the definitions of mutually exclusive and non-mutually exclusive events. • Explain the definition of conditional probability. • Explain the definition of randomness. • Explain probability events and their calculations. • Explain how to calculate and interpret the probability of events. • Explain how to apply basic probability. A clear understanding of the basic statistical terms and concepts presented in Chapter 4 will help prepare you to advance in this course and learn more complex statistical calculations and specific statistical tests. You should refer back to Chapters 1, 2, and 3 and understand all concepts presented thus far. As you study, you should pay particular attention to the definitions and you should have an understanding of how a probability is calculated and applied. You should pay particular attention to the probability events their corresponding calculations. Study Clues • Mutually exclusive: When two events or outcomes cannot occur at the same time, they are said to be mutually exclusive. However, each event has the same chance or probability of occurring. The classic example of this is tossing a coin. You have a 50% chance of getting heads or tails, but not both at the same time. • Not mutually exclusive: This occurs when one or more event can occur at the same time. If you are giving a survey, you can expect to have multiple outcomes from the population if you ask the question “Howwell do you enjoy statistics?” You can also havemutually non -exclusive events if you draw a card from a deck and determine the probability that it will be either black or red and a face card. • Conditional probability: Some of the outcomes for (A) will occur if some of the outcomes for (B) occur. With this, A is partially dependent on B. If some of the outcomes for B do not occur, 4.1 Basic Terms

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