Grade 11 Mathematics Unit 8 : Probability

This unit introduces you to probability, the branch of mathematics that deals with the likelihood of events occurring. You’ll learn the essential tools for counting outcomes and use them to calculate and interpret the chances of everything from a coin flip to real-world events.

Chapter 8.2 & 8.3 – Counting: Permutations and Combinations

Before you can calculate probability, you need to know how to count all the possibilities.

• Learn the Fundamental Principle of Counting (Multiplication Principle) to determine the total number of outcomes for a sequence of events.
• Master the two key methods for counting arrangements:
  • Permutations: Used when the order of selection matters (e.g., arranging books on a shelf).
  • Combinations: Used when the order of selection does not matter (e.g., choosing a committee from a group of people).

Chapter 8.4 – Binomial Theorem

This section explores a powerful algebraic tool for expanding expressions, which has strong ties to probability.

• Understand the Binomial Theorem as a quick way to expand expressions with two terms raised to a power.
• See the connection between the theorem’s coefficients and Pascal’s Triangle as well as combinations.

Chapter 8.5 & 8.6 – Random Experiments and Events

Learn the formal language used to describe and analyze uncertain situations.

• Define key terms like random experiment, sample space (all possible outcomes), and event (a specific outcome you’re interested in).
• Distinguish between different types of events, such as simple, compound, mutually exclusive, and independent events.

Chapter 8.7 – Probability of an Event

This chapter covers the core calculation of probability.

• Calculate the probability of an event using the fundamental formula, which is the ratio of the number of favorable outcomes to the total number of possible outcomes.
• Represent probabilities correctly as fractions, decimals (between 0 and 1), and percentages (between 0% and 100%).
• Understand that a probability of 0 means the event is impossible, and a probability of 1 means the event is certain.

Chapter 8.8 – Real-life Application of Probability

See how probability is a critical tool in science, business, and everyday life.

• Analyze how probability is used in insurance to assess risk.
• Explore its role in weather forecasting, genetics, and games of chance.
• Solve practical problems by applying the counting and probability principles you’ve learned.

Learning Outcomes

By the end of this unit, you’ll be able to:

• Use principles of counting, including permutations and combinations.
• Understand the Binomial Theorem.
• Calculate the probability of simple and compound events.
• Represent probabilities as fractions, decimals, and percentages.
• Apply probability concepts to solve real-life problems.