Lesson Notes By Weeks and Term v4 - SHS 3
PROBABILITY/CHANCE
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PROBABILITY/CHANCE
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Subject: Mathematics
Class: SHS 3
Term: 2nd Term
Week: 20
Grade code: 3.4.2.LI.2
Strand code: 4
Sub-strand code: 2
Content standard code: 3.4.2.CS.1
Indicator code: 3.4.2.LI.2
Theme: MAKING SENSE OF AND USING DATA
Subtheme: PROBABILITY/CHANCE
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Probability is not just a topic in a mathematics textbook; it is a way of understanding the world around us. In Ghana, we informally use probability every day. We think about the chance of rain during the rainy season, the likelihood of 'dumsor' on a hot evening, or the probability of the Black Stars winning a crucial match. This lesson will formalise that thinking. We will learn the mathematical rules that govern the chances of single and multiple events happening. By understanding these rules, we can make more informed decisions in areas ranging from business and health to agriculture and sports.
This lesson builds on your basic understanding of probability: `P(Event) = (Number of favourable outcomes) / (Total number of possible outcomes)`
We will now explore situations involving *two* events. A. Independent vs. Dependent Events Independent Events: Two events are independent if the outcome of the first event does not affect the outcome of the second event. Think: The events have no memory of each other. Ghanaian Example: The probability that it rains in Accra today is independent of the probability that a student in Navrongo passes their WASSCE Core Maths paper. The two events are unconnected. Classic Example: Tossing a coin and then rolling a die. Getting a "Head" does not change the probability of rolling a "6". Dependent Events: Two events are dependent if the outcome of the first event does affect the outcome of the second event. Think: The second event's probability depends on what happened first. This often occurs in situations "without replacement". Ghanaian Example: Imagine a bowl containing 5 pieces of meat and 3 pieces of fish. If your brother takes a piece of meat first (and eats it), the probability of you picking meat next has changed because there are fewer pieces of meat and fewer total pieces in the bowl. Key Phrase: "Without replacement". B. The Multiplication Law (for "AND" Events)
This law is used when we want to find the probability of Event A AND Event B both happening. For Independent Events If A and B are independent, the probability of both occurring is the product of their individual probabilities. `P(A and B) = P(A) × P(B)`