Lecture Notes: In-Class Activity 7C

Introduction

• Focus on using concepts over formulas.
• Information will be presented in tables.
• Goal: Answer questions using tables, not theoretical values.

Basics of Probability

• Probability of an event = Number of favorable outcomes / Total number of outcomes.
• In a two-way table:
  • Subtotal / Grand total for basic probability.

Conditional Probability

• Probability of an event given another event has occurred.
• Changes focus from grand total to a subtotal.
• Example: Probability of being left-handed given that the person is female.

Examples

• Bike Riding in Snow:
  • Probability is low; condition: snow on the ground.
• Political Beliefs:
  • Example of likelihood of holding conflicting beliefs based on known beliefs.

Definitions

• Mutually Exclusive Events: Cannot happen at the same time.
• Independent Events: One event does not affect the probability of the other.

Tests

• Independence: Does knowing event A help predict event B?
• Mutually Exclusive: No overlap or shared outcomes.

Two-Way Tables

• Tables with rows and columns for different categories (e.g., energy spending, child care spending).
• Subtotals and grand totals.
• Use for calculating probabilities.

Calculating Probabilities

• Use table to find simple and conditional probabilities.
• Example: Probability of thinking U.S. spends too much on child care.

Conditional Probability Calculation

• Focus on the given condition; this becomes the new denominator (subtotal).
• Example: Probability of spending too little on energy given too little on child care.

Test of Independence

• Formula: P(A given B) = P(A)
• Example: Test for race and political affiliation.

Mutually Exclusive vs. Independent

• Mutually exclusive: Events cannot occur simultaneously; related and not independent.
• Example: Being pregnant and male are mutually exclusive.

Practice Problems

• Fill in probability tables and answer questions based on conditions.
• Use subtotals for conditional probabilities.

Conclusion

• Importance of understanding the difference between independent and mutually exclusive events.
• Practice recommended with 20-minute to 1-hour breaks to improve retention.