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4.1 Introducing Statistics: Random and Non-Random Patterns?

Part of Probability, Random Variables, and Probability Distributions in AP® Statistics. Read the opening section, then create a free account for the full interactive lesson, practice, and progress tracking.

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What is Probability?

Probability

Key ideas:

  • P(A)=0{P(A) = 0} → event A never occurs
  • P(A)=1{P(A) = 1} → event A always occurs
  • 0<P(A)<1{0 < P(A) < 1} → event A sometimes occurs

The Law of Large Numbers

P(A)≈number of times A occurrednumber of trialsas trials→∞P(A) \approx \frac{\text{number of times A occurred}}{\text{number of trials}} \quad \text{as trials} \to \infty

Misconception — The Gambler's Fallacy: Gambler's fallacy "I've flipped tails 5 times in a row, so I'm 'due' for heads." — WRONG! Each flip is independent.

In this unit

12 lessons

  1. 4.1Introducing Statistics: Random and Non-Random Patterns?This lesson
  2. 4.2Estimating Probabilities Using SimulationPreview lesson
  3. 4.3Introduction to ProbabilityPreview lesson
  4. 4.4Mutually Exclusive EventsPreview lesson
  5. 4.5Conditional ProbabilityPreview lesson
  6. 4.6Independent Events and Unions of EventsPreview lesson
  7. 4.7Introduction to Random Variables and Probability DistributionsPreview lesson
  8. 4.8Mean and Standard Deviation of Random VariablesPreview lesson
  9. 4.9Combining Random VariablesPreview lesson
  10. 4.10Introduction to the Binomial DistributionPreview lesson
  11. 4.11Parameters for a Binomial DistributionPreview lesson
  12. 4.12The Geometric DistributionPreview lesson

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