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...
Advanced Topics

Probability Distributions

What Are Probability Distributions?

A probability distribution describes how probabilities are spread over all possible outcomes of a random experiment.

Discrete vs. Continuous

  • Discrete distributions have a finite or countable number of outcomes (e.g., rolling dice).
  • Continuous distributions have outcomes over a range (e.g., height, time).

Examples of Distributions

  • Uniform Distribution: All outcomes are equally likely.
  • Binomial Distribution: Counts successes in repeated experiments.
  • Normal Distribution: The famous "bell curve" seen in measurements like height.

Probability distributions help us summarize lots of information in a compact way, making it easier to predict, analyze, and make decisions.

Examples

  • The probability of each face in a dice roll forms a uniform distribution.

  • The distribution of students’ test scores often looks like a bell curve (normal distribution).

In a Nutshell

Probability distributions show how probabilities are assigned to different outcomes.

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Probability in Games and Sports