Scenario: Board Games - Understand probability concepts through dice games and card games!
You're playing a board game that uses a standard 6-sided die. You need to understand the probability of different outcomes to make strategic decisions.
Questions:
1. What is the probability of rolling a 3?
2. What is the probability of rolling an even number?
3. What is the probability of rolling a number greater than 4?
Standard 6-sided die faces
Question 1: Probability of rolling a 3
Possible outcomes: 1, 2, 3, 4, 5, 6 (6 total)
Favorable outcomes: 3 (1 total)
Probability = 1/6 ≈ 0.167 or 16.7%
Question 2: Probability of rolling an even number
Possible outcomes: 1, 2, 3, 4, 5, 6 (6 total)
Favorable outcomes: 2, 4, 6 (3 total)
Probability = 3/6 = 1/2 = 0.5 or 50%
Question 3: Probability of rolling a number greater than 4
Possible outcomes: 1, 2, 3, 4, 5, 6 (6 total)
Favorable outcomes: 5, 6 (2 total)
Probability = 2/6 = 1/3 ≈ 0.333 or 33.3%
The likelihood that an event will occur, expressed as a number between 0 and 1.
Formula: P(event) = Favorable outcomes ÷ Total outcomes
All possible results of an experiment or event.
Example: Rolling a die has 6 outcomes: 1, 2, 3, 4, 5, 6
The specific outcomes that you want to happen.
Example: Rolling an even number: 2, 4, 6
A specific outcome or set of outcomes you're interested in.
Example: "Rolling a 3" or "Rolling an even number"
Will never happen
Example: Rolling a 7 on a standard die
Will always happen
Example: Rolling a number 1-6 on a standard die
A bag contains 3 red marbles, 2 blue marbles, and 5 green marbles. What is the probability of drawing a red marble?
Your solution:
You flip a coin twice. What is the probability of getting heads both times?
Your solution: