Lesson Notes By Weeks and Term v4 - SHS 1
PROBABILITY/CHANCE
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PROBABILITY/CHANCE
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Subject: Mathematics
Class: SHS 1
Term: 2nd Term
Week: 20
Grade code: 1.4.2.LI.3
Strand code: 4
Sub-strand code: 2
Content standard code: 1.4.2.CS.1
Indicator code: 1.4.2.LI.3
Theme: MAKING SENSE OF AND USING DATA
Subtheme: PROBABILITY/CHANCE
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Probability is the mathematics of chance. In our daily lives in Ghana, we are constantly faced with uncertainty. Will it rain in Accra today? Will the Black Stars win their next match? Will the price of kenkey go up next week? Probability gives us a way to measure and understand these uncertainties. This lesson focuses on a specific type of situation: independent events, where the outcome of one event has absolutely no effect on the outcome of another. Understanding this concept helps us make better predictions and decisions in games, business, and even in personal planning.
A. What is Probability? (A Quick Recap) Probability is a number between 0 and 1 that tells us how likely an event is to happen. A probability of 0 means the event is impossible. (e.g., The sun rising from the west). A probability of 1 means the event is certain. (e.g., You will get older tomorrow). A probability of 0.5 or 1/2 means the event has an even chance of happening. (e.g., Getting a head when you toss a fair coin).
We calculate basic probability as: $$ \text{Probability} = \frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}} $$ B. What are Independent Events? This is the core idea for today. Two events are independent if the outcome of the first event does not influence or change the probability of the second event.
Think about it this way: Example 1: You toss a 1 cedi coin and get heads. You toss it again. Does the first result (heads) change the chances of getting heads on the second toss? No. The coin doesn't remember what happened before. The probability is still 1/2. These are independent events. Example 2: In a bag, there are 5 red balls and 3 blue balls. Kofi picks a ball, sees the colour, and puts it back. Ama then picks a ball. Did Kofi's pick affect Ama's chances? No. Because he put the ball back, the bag is exactly the same for Ama. These are independent events.
Contrast with Dependent Events: If Kofi picked a red ball and *did not* put it back, the bag would now have 4 red balls and 3 blue balls. The total is now 7. Ama's chances have changed because of what Kofi did. This would be a *dependent* event. We will focus only on independent events today. C. The Multiplication Rule for Independent Events When we want to find the probability of two independent events *both* happening, we multiply their individual probabilities.