AP Statistics: Probability Review

Introduction

• Focus on probability topics for the AP Statistics test.
• Five key topics to be covered:
  1. 'Or' vs 'And' Probability
  2. Two-Way Table Probability
  3. Conditional Probability with Tree Diagrams
  4. Multiplication of Independent Events
  5. Probability with Normal Model
• Separate video for the binomial model.

Understanding Probability

• Probability is the long-run relative frequency of an event.
• Law of Large Numbers: True probability reveals itself after many trials.
• Example: Coin toss probability and how sample size affects outcomes.

Or vs And Probability

• Addition Rule: Probability of A or B = P(A) + P(B) - P(A and B)
• 'Or' means A or B or both.
• Venn Diagram Introduction:
  • Overlap of A and B counts twice; subtract it to get correct probability.

Mutually Exclusive Events

• Two events cannot occur at the same time.
• If A and B are mutually exclusive, P(A or B) = P(A) + P(B).
• Probability of A and B = 0 if mutually exclusive.

Independent Events

• Outcome of A does not impact outcome of B.
• If A and B are independent, P(A and B) = P(A) * P(B).
• Use this formula only if independence is confirmed.
• Mutually exclusive events cannot be independent.*

Two-Way Tables

• Easy to work with for probability questions.
• Example problems using a table of education level and news source.
• Finding probability of events and conditional probabilities.

Conditional Probability

• Dependent events where one outcome impacts another.
• Formula: P(A|B) = P(A and B) / P(B)
• Use a two-way table for practical examples.

Conditional Probability with Tree Diagrams

• Useful for visualizing conditional probability scenarios.
• Example problem: Diagnosing dogs with heartworm.
• Understanding false positives and negatives via tree diagrams.

Multiplying Probabilities for Multiple Events

• For multiple sequential events, multiply probabilities.
• Consider whether events are independent or conditional.
• Example: Probability of selecting boys from a group sequentially.

Probability and the Normal Model

• Probability questions related to the normal distribution.
• Use normalcdf function on calculators.
• Mention of binomial probability as a separate topic.

Conclusion

• Emphasis on understanding different probability scenarios and calculations.
• Recommendation to check out additional resources for binomial probability and normal models.