Lesson 5-3: Probability Basics

Scenario: Games & Experiments - Learn probability concepts through fun games and experiments!

Duration: 65-80 minutesScenario: Games & Experiments

Learning Objectives

Understand basic probability concepts
Calculate simple probabilities
Distinguish between theoretical and experimental probability
Apply probability to games and experiments

Games & Experiments Scenario

The Problem

You're playing a board game with friends. The game involves rolling a standard 6-sided die and spinning a spinner with 4 equal sections (red, blue, green, yellow). You need to calculate the probability of different outcomes to make strategic decisions.

Game Challenge:
Calculate the probability of rolling a 3 on the die and spinning red on the spinner.

Game Setup

6-sided Die:

Faces: 1, 2, 3, 4, 5, 6

4-section Spinner:

Colors: Red, Blue, Green, Yellow

Probability Basics

What is Probability?

Probability: A measure of how likely an event is to occur.

Probability is expressed as a number between 0 and 1, or as a percentage between 0% and 100%.

Probability Scale

0 (Impossible)0.5 (Equally Likely)1 (Certain)

0%50%100%

Theoretical Probability

Formula

Theoretical Probability: P(Event) = Number of favorable outcomes ÷ Total number of possible outcomes

Solving the Game Problem

Find the probability of rolling a 3 on the die AND spinning red on the spinner.

Step 1: Find probability of rolling a 3

P(rolling 3) = 1 favorable outcome ÷ 6 possible outcomes = 1/6

Step 2: Find probability of spinning red

P(spinning red) = 1 favorable outcome ÷ 4 possible outcomes = 1/4

Step 3: Find probability of both events (AND)

P(3 AND red) = 1/6 × 1/4 = 1/24 ≈ 0.042 or 4.2%

Experimental Probability

What is Experimental Probability?

Experimental Probability: Probability based on actual results from experiments or trials.

Formula: P(Event) = Number of times event occurred ÷ Total number of trials

Coin Toss Experiment

You flip a coin 20 times and get heads 12 times. What is the experimental probability of getting heads?

Given: 12 heads out of 20 flips

Calculation: P(heads) = 12 ÷ 20 = 0.6 or 60%

Note: This is close to the theoretical probability of 50%, but not exactly the same due to chance.

Probability Rules

Key Rules

AND Events

Multiply the probabilities

P(A AND B) = P(A) × P(B)

OR Events

Add the probabilities (if mutually exclusive)

P(A OR B) = P(A) + P(B)

Example: OR Events

What is the probability of rolling a 2 OR a 4 on a 6-sided die?

P(rolling 2): 1/6

P(rolling 4): 1/6

P(2 OR 4): 1/6 + 1/6 = 2/6 = 1/3 ≈ 0.333 or 33.3%

Practice Problems

Problem 1: Simple Probability

A bag contains 3 red marbles, 2 blue marbles, and 5 green marbles. What is the probability of drawing a red marble?

Your solution:

Problem 2: Compound Probability

You roll a die and flip a coin. What is the probability of rolling an even number AND getting heads?

Your calculation:

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