Probability Theory

Probability Theory explores the mathematical framework for quantifying uncertainty and making informed decisions based on random events.

Random Experiments and EventsCalculating ProbabilityTypes of Probability
Conditional ProbabilityIndependent and Dependent EventsProbability Distributions
Probability in Games and SportsProbability in Weather ForecastingProbability in Medicine and Health
Read the Question CarefullyDraw a Diagram or Table
Random Experiments a...Calculating Probabil...Types of ProbabilityConditional Probabil...Independent and Depe...Probability Distribu...Probability in Games...Probability in Weath...Probability in Medic...Read the Question Ca...Draw a Diagram or Ta...
Basic Concepts

Calculating Probability

How Do We Calculate Probability?

Probability tells us how likely an event is to happen, and it's always a number between 0 (impossible) and 1 (certain). If every outcome is equally likely, the probability of an event \(A\) is:

\[ P(A) = \frac{\text{Number of outcomes in } A}{\text{Total number of possible outcomes}} \]

Probability Rules

  • The probability of any event is between 0 and 1.
  • The sum of probabilities of all possible outcomes is 1.
  • The probability of the event "not \(A\)" is \(1 - P(A)\).

Using Probability in Everyday Life

We use probability to predict the weather, decide whether to take an umbrella, or figure out the odds of winning a board game!

Examples

  • The chance of rolling a 3 on a six-sided die is 1/6.

  • The probability of drawing a heart from a standard deck of cards is 13/52 = 1/4.

In a Nutshell

Probability measures how likely an event is to occur, using straightforward rules and simple math.

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Types of Probability