Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Define terms: experiment, outcome, sample space, event.
• Calculate the probability of a simple event.
• Represent probabilities as fractions, decimals, and percentages.
• Conduct and interpret simple probability experiments.

Lesson summary

Probability is the study of how likely events are to happen. It’s a crucial skill for making informed decisions in everyday life. Think about deciding whether to buy a lottery ticket, assessing the risk of investing in a small business in your community, or even just deciding whether to take an umbrella when the weather forecast is uncertain. In South Africa, understanding probability can help us navigate complex social and economic situations, from understanding crime statistics to making informed choices about health and finance. This week, we'll focus on the basic concepts of probability and explore simple experiments to understand how probability works in practice.

Lesson notes

Here's a breakdown of the core concepts you need to understand: Experiment: An activity that produces outcomes. For example, flipping a coin, rolling a die, or drawing a card from a deck.

Outcome: A possible result of an experiment. If you flip a coin, the possible outcomes are "heads" or "tails." If you roll a die, the possible outcomes are 1, 2, 3, 4, 5, or

6. Sample Space: The set of all possible outcomes of an experiment. We often use the letter "S" to represent the sample space. For example, for flipping a coin, S = {Heads, Tails}. For rolling a die, S = {1, 2, 3, 4, 5, 6}.

Event: A specific outcome or a set of outcomes that we are interested in. For example, rolling an even number on a die is an event. The event includes the outcomes {2, 4, 6}. Drawing a king from a deck of cards is an event.

Probability: A measure of how likely an event is to occur. Probability is expressed as a fraction, decimal, or percentage, and its value always lies between 0 and 1 (or 0% and 100%). A probability of 0 means the event is impossible, and a probability of 1 means the event is certain.

Equally Likely Outcomes: When each outcome in the sample space has the same chance of occurring. For example, a fair coin has equally likely outcomes (heads or tails). A fair die has equally likely outcomes (1, 2, 3, 4, 5, or 6).

Calculating Probability: The probability of an event (E) occurring is calculated as follows: P(E) = (Number of favourable outcomes for event E) / (Total number of possible outcomes in the sample space)

Important Notes: The probability of an event not occurring is 1 minus the probability of the event occurring. P(not E) = 1 - P(E). Probabilities can be expressed as fractions, decimals, or percentages. To convert a fraction to a decimal, divide the numerator by the denominator. To convert a decimal to a percentage, multiply by

1

0

0. When dealing with multiple events, be careful to identify whether the events are independent (one event does not affect the other) or dependent (one event affects the other). We'll cover dependent events in more detail later.

Worked example

Example 1: Flipping a Coin

What is the probability of flipping a fair coin and getting "heads"?

Experiment: Flipping a coin

Sample Space: S = {Heads, Tails}

Event (E): Getting "heads"

Number of favourable outcomes for event E: 1 (Heads)

Total number of possible outcomes: 2 (Heads, Tails)

Probability: P(Heads) = 1/2 = 0.5 = 50%

Therefore, the probability of getting "heads" when flipping a fair coin is 1/2, 0.5, or 50%.

Example 2: Rolling a Die