Understanding Equally Likely Outcomes and Fairness
Grade 7 students in Big Ideas Math Advanced 2 (Chapter 15: Probability and Statistics) learn that equally likely outcomes are the foundation for the basic probability formula. The formula P = favorable/total only applies when each outcome has the same chance of occurring.
Key Concepts
Outcomes are equally likely when each outcome has the same chance of occurring. The basic probability formula $P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}$ only applies when all outcomes are equally likely.
Common Questions
What does equally likely outcomes mean in probability?
Equally likely outcomes means each outcome has the same probability of occurring. Rolling a fair die gives equally likely outcomes since each face (1-6) has the same 1/6 chance.
How do you know if outcomes are equally likely?
Outcomes are equally likely when the chance of each is identical—fair dice, fair coins, and random selections from identical items all produce equally likely outcomes.
When can you NOT use the basic probability formula P = favorable/total?
When outcomes are not equally likely (e.g., a weighted die or a bag with different numbers of each color). In these cases, each outcome has a different probability.
What chapter in Big Ideas Math Advanced 2 covers equally likely outcomes?
Chapter 15: Probability and Statistics in Big Ideas Math Advanced 2 (Grade 7) covers equally likely outcomes and fairness in probability.
What makes a game fair in probability?
A game is fair when each player has an equally likely chance of winning. This requires that all relevant outcomes have equal probability.