## 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)

- Random phenomenon
- 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

- Coin Toss – see Example 4.8 on p. 245
- Video
- Exercise 4.21 on p. 255

- Sample Space

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