Lesson 14: Intro to Probability and Probability Models

October 17, 2016

Mon, Oct 17

Review:

• Make-up Exams
• Samples, Surveys and Political Forecasting
• Election Forecast Update

Presentation:

• Intro to Probability
  • Topic worthy of its own course
  • Simulation of outcomes
    • Random phenomenon
      • Individual outcomes are uncertain
      • Regular distribution of outcomes in large number of trials
    • Independent trials
    • Repetition – note coin tosses required to reach 0.5 probability (p. 238)
  • Video
• Probability Models
  • Sample Space
    • Discrete vs Continuous
    • All possible Outcomes
  • Probability Rules (see p. 246)
    • Rule 1: Any probability is a number between 0 and 1. Or, mathematically, 0 ≤ P(A) ≤ 1
    • Rule 2: All possible outcomes together must have probability = 1.
    • Rule 3: If events A and B have no outcomes in common, they are disjoint and P(A or B) = P(A) + P(B). This is the addition rule.
    • Rule 4: The complement of an event, A = 1 – P(A)
    • Rule 5: If events A and B are independent then P(A and B) = P(A)*P(B). This is the multiplication rule.
  • Examples:
    • Coin Toss – see Example 4.8 on p. 245
      • Flip a coin 4 times. Event A = toss is “Heads” exactly 2 times. What is P(A)?
      • Step 1: Define the Sample Space (all possible outcomes)
      • Step 2: Identify the set of outcomes that satisfy Event A
      • Step 3: P(A) = Number of Event A outcomes ÷ Number of possible outcomes
    • Roll a pair of dice
      • Define Event A (e.g., roll = 7). What is P(A)?
      • Follow Steps 1-3 above
  • Video
  • Exercise 4.21 on p. 255

Activity:

• Complete Exercises 4.22, 4.24, 4.26 on pp. 255-256

Assignment:

• Read pp. 237-241, Intro to Probability
• Read pp. 242-248, Probability Models
• Read Where the Race Stands with 3 Weeks to Go by Nate Silver