Lesson Notes By Weeks and Term v4 - SHS 3
MAKING PREDICTIONS WITH DATA
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MAKING PREDICTIONS WITH DATA
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Subject: Additional Mathematics
Class: SHS 3
Term: 2nd Term
Week: 15
Grade code: 3.4.2.LI.3
Strand code: 4
Sub-strand code: 2
Content standard code: 3.4.2.CS.1
Indicator code: 3.4.2.LI.3
Theme: HANDLING DATA
Subtheme: MAKING PREDICTIONS WITH DATA
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In our daily lives, we often make judgments based on new information. For example, the chance of the Black Stars winning a match might change if we find out their star player is injured. The probability of getting to school on time changes if you know there is heavy traffic on the N1 highway. This idea of probability changing based on a known condition or event is called Conditional Probability. It is a powerful tool for making smarter predictions and decisions in fields like medicine, business, agriculture, and even sports. This lesson will equip you with the skills to model and solve such problems.
a) Recap: Independent vs. Dependent Events
To understand conditional probability, we must first recall the difference between independent and dependent events. Independent Events: Two events are independent if the outcome of one event does not affect the outcome of the other. Example: Tossing a coin and rolling a die. The result of the coin toss has no impact on the number that shows on the die. For independent events A and B: P(A and B) = P(A) × P(B) Dependent Events: Two events are dependent if the outcome of the first event affects the outcome of the second. This is where conditional probability becomes essential. Example: Drawing two cards from a deck *without replacement*. The probability of drawing a King on the second draw depends on whether a King was drawn on the first draw. b) What is Conditional Probability?
Conditional probability is the probability of an event (let's call it A) occurring, *given that* another event (B) has already occurred.
The key phrase is "given that". This new information reduces our "sample space" – the set of all possible outcomes.