## Lesson 7: Probability Models and Dice Game Simulation

February 3, 2020

Review:

- Quiz 03
- Intro to Probability

Presentation:

- Probability Models
- Sample Space
- Discrete vs Continuous
- All possible Outcomes

- Probability Rules (see p. 246 in textbook)
- 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.

- How to calculate discrete probability:
- 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
- Example:
- Roll a pair of dice
- Define Event A (e.g., roll = 7). What is P(A)?
- Follow Steps 1-3 above
- Step 1: 36 possible outcomes
- Step 2: Roll a 7 with 1+6, 2+5, 3+4, 4+3, 5+2, 6+1 (6 possible outcomes resulting in a roll of 7)
- Step 3: P(A): 6/36 = 1/6 =
**0.167**

- Roll a pair of dice

- Demonstrate Simulation of rolling a pair dice in Sheets
- Lucky 7 game
- Roll a 7, win bet
- Roll anything else (other than a 7), lose bet

- Lucky 7 game

Assignment:

- Create your own Dice Simulation
- Simulate “Pass”, a simplified version of Craps

- Rules of Pass
- Player rolls a pair of six-sided dice
- Player …
- wins if the roll is 7 or 11
- loses if the roll is 2, 3 or 12
- ties if the roll is 4, 5, 6, 8, 9 or 10

- Simulate 100 games

- Calculate % wins, % losses and % ties