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: 11
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: HANDLING DATA
Subtheme: MAKING PREDICTIONS WITH DATA
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In our daily lives in Ghana, we are constantly making predictions based on existing information. A farmer in the Ashanti region might ask, "What is the chance of a good cocoa harvest *given that* the rains started early this year?" A student might wonder, "What is the probability I will pass my WASSCE Core Maths paper *given that* I have solved all the past questions from the last ten years?" This type of "probability given that..." is what we call Conditional Probability. It is a powerful tool for making more accurate predictions because it forces us to update our calculations based on new evidence or conditions.
A. What is Conditional Probability?
Let's start with a simple idea. Imagine you have a bag with 5 red balls and 5 blue balls (10 total). The probability of picking a red ball is `P(Red) = 5/10 = 1/2`.
Now, imagine your friend picks a ball, doesn't replace it, and tells you, "I picked a blue ball." There are now 9 balls left (5 red, 4 blue). If you pick next, what is the probability of picking a red ball? The probability is now `5/9`.
Notice how the probability changed once you received new information. The initial condition (picking a blue ball first) changed the "sample space" (the total possible outcomes) for the second event.