Lesson Notes By Weeks and Term v4 - JHS 3

Lesson Video

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Performance objectives

• Define probability and dependent events.
• Conduct a probability experiment involving two dependent events.
• Calculate the probability of dependent events.
• Relate probability to real-life situations.

Lesson summary

This lesson introduces learners to the concept of dependent events in probability. We will explore situations where the outcome of a first event directly affects the possible outcomes, and therefore the probability, of a second event. In our daily lives in Ghana, we often face situations where what happens first changes our chances for what happens next—from picking items from a market stall to playing games like Oware. Understanding dependent events helps us make smarter decisions when faced with uncertainty. This lesson will move from theory to a hands-on experiment to make the concept practical and clear.

Lesson notes

A. Recap: What is Probability?

Probability is the measure of how likely an event is to happen. It is calculated as: $$ \text{Probability (P)} = \frac{\text{Number of Favourable Outcomes}}{\text{Total Number of Possible Outcomes}} $$ For example, if there are 5 mangoes and 3 oranges in a basket, the probability of picking a mango is 5/8. B. Independent vs. Dependent Events

To understand dependent events, we must first know what they are *not*. Independent Events: Two events are independent if the outcome of the first event does not affect the outcome of the second event. Example: Tossing a coin twice. The result of the first toss (Heads or Tails) has no effect on the probability of getting Heads or Tails on the second toss. Calculation: P(A and B) = P(A) × P(B) Dependent Events (Our Focus Today): Two events are dependent if the outcome of the first event does affect the outcome of the second event. This usually happens in situations described as "without replacement". When you take something out and don't put it back, the total number of possible outcomes changes for the next selection. Key Idea: The sample space (total possible outcomes) for the second event is smaller or different because of what happened in the first event. Calculation: P(A and B) = P(A) × P(B | A) P(B | A) means "the probability of event B happening, *given that* event A has already happened." We don't need to focus on the formal notation, but on the logic behind it. C. Worked Example 1: Simple Calculation

Imagine a small class with 4 boys and 6 girls. The teacher wants to select two students at random to be class prefects. What is the probability that both students selected are girls?