Counting and Probability - Introduction

You've probably heard people say things like:

• The chance of rain tomorrow is 75%.
• Teen mothers who live with their parents are less likely to use marijuana than teen moms in other living arrangements.
• He won the lottery!
• There is longstanding evidence that children raised by single parents are more likely to perform poorly in school and partake in ‘deviant’ behaviors such as smoking, sex, substance use and crime at young ages. [Source]
• She'll probably take the offer.
• Life insurance is so expensive for someone over 50.

All of these statements are about probability. We see words like "chance", "less likely", "probably" since we don't know for sure something will happen, but we realise there is a very good chance that it will.

In the case of the lottery (or Toto), there is a very good chance that some things (like a win) will not happen!

To decide "how likely" an event is, we need to count the number of times an event could occur and compare it to the total number of possible events. Such a comparison is called the probability of the particular event occurring.

The mathematical theory of counting is known as combinatorial analysis.

In this Chapter

Counting

• 1. Factorial Notation
• 2. Basic Principles of Counting
• 3. Permutations
• 4. Combinations

Probability

• 5. Introduction to Probability Theory
• 6. Probability of an Event
  • Singapore TOTO
  • Probability and Poker

Probabilities of 2 or more Events

• 7. Conditional Probability
• 8. Independent and Dependent Events
• 9. Mutually Exclusive Events
• 10. Bayes’ Theorem

Probability Distributions

• 11. Probability Distributions - Concepts
• 12. Binomial Probability Distributions
• 13. Poisson Probability Distribution
• 14. Normal Probability Distribution
  • The z-Table

We begin the chapter with a reminder about Factorial Notation »