Lesson Notes By Weeks and Term v4 - JHS 2

Lesson Video

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Performance objectives

• Define probability and independent events.
• Conduct an experiment with two independent events.
• Calculate the combined probability of two independent events.
• Apply probability to solve real-life problems.

Lesson summary

Probability is the mathematics of chance. It helps us understand and predict how likely something is to happen. In our daily lives in Ghana, we are surrounded by chance. Will the Black Stars win their next match? Will it rain in the afternoon so we can plant our maize? Will I be the one chosen to answer the next question? By understanding probability, we can move from simple guessing to making more informed decisions. This lesson focuses on what happens when two separate, or 'independent', events occur, like tossing a coin and then rolling a die.

Lesson notes

Part 1: The Basics of Probability (Recap) What is Probability? It's a measure of how likely an event is to happen. We write it as a fraction, decimal, or percentage. Probability = (Number of favourable outcomes) / (Total number of possible outcomes) Key Terms: Experiment: An action where the result is uncertain. (e.g., tossing a coin). Outcome: A single possible result of an experiment. (e.g., getting a 'Head'). Sample Space (S): The set of ALL possible outcomes. For a die, S = {1, 2, 3, 4, 5, 6}. For a coin, S = {Head, Tail}. Event (E): A specific outcome or set of outcomes you are interested in. (e.g., the event of rolling an even number on a die, E = {2, 4, 6}).

Example (Single Event): What is the probability of rolling a 4 on a standard six-sided die? Favourable outcome = {4} (There is only one '4') Total possible outcomes = {1, 2, 3, 4, 5, 6} (There are six faces) P(rolling a 4) = 1/6 Part 2: Two Independent Events (The Core of the Lesson) Definition of Independent Events: Two events are independent if the outcome of the first event does not affect the outcome of the second event. They have no influence on each other. Real-life Examples: Tossing a coin and then rolling a die. The coin landing on 'Heads' does not change the possible numbers the die can land on. Spinning a spinner twice. The first spin does not affect the second spin. Picking a ball from a bag, putting it back (replacement), and then picking a second ball. Because the first ball was returned, the conditions for the second pick are exactly the same as the first. The Multiplication Rule for Independent Events: To find the probability of two independent events (Event A and Event B) both happening, you multiply their individual probabilities.

P(A and B) = P(A) × P(B)

Think of the word "AND" as a signal to "MULTIPLY". Worked Examples