Lesson Notes By Weeks and Term v4 - SHS 1
MAKING PREDICTIONS WITH DATA
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MAKING PREDICTIONS WITH DATA
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Subject: Additional Mathematics
Class: SHS 1
Term: 2nd Term
Week: 20
Grade code: 1.4.2.LI.5
Strand code: 4
Sub-strand code: 2
Content standard code: 1.4.2.CS.1
Indicator code: 1.4.2.LI.5
Theme: HANDLING DATA
Subtheme: MAKING PREDICTIONS WITH DATA
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This lesson introduces the fundamental language of probability. Probability is a branch of mathematics that helps us understand and quantify uncertainty or chance. In our daily lives in Ghana, we are constantly making predictions: "Will it rain today during the market hours?", "What are the chances that the Black Stars will win their next match?", "If I take a tro-tro now, am I likely to get to Accra Central on time?". By understanding the basic terminologies, we build the foundation needed to analyse these situations mathematically and make more informed predictions. This lesson is not about calculation, but about learning the correct words to describe situations involving chance.
This section breaks down the essential vocabulary for understanding probability. We will use the simple experiment of rolling a standard six-sided die, like the one used in a game of Ludo, to illustrate these concepts. a. Probability Definition: Probability is a measure of how likely it is that something will happen. It is a number between 0 and 1 (or 0% and 100%). Explanation: 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., the sun will rise tomorrow). A probability of 0.5 (or 1/2 or 50%) means the event is just as likely to happen as not to happen (e.g., a fair coin landing on heads). b. Experiment Definition: An experiment is any process or action that has a result that cannot be known with certainty beforehand. Explanation: It's the "thing you do" to see what will happen. It must be repeatable and have a well-defined set of possible results. Ghanaian Examples: Tossing a 1 Ghana Cedi coin to decide who starts a football game. Playing a game of "pick-a-straw" where one is shorter than the others. A student randomly choosing a question from a set of past WASSCE questions in a box. c. Trial Definition: A trial is a single performance or run of an experiment. Explanation: If you perform an experiment multiple times, each time is called a trial. Ghanaian Examples: If the experiment is "tossing a coin three times," then the *first toss* is one trial, the *second toss* is another trial, and the *third toss* is a third trial. If the experiment is "rolling a die," each single roll of the die is a trial. d. Outcome Definition: An outcome is a single possible result of a trial. Explanation: It's one specific thing that can happen when you perform the experiment once. Ghanaian Examples: In the experiment of tossing a 1 Cedi coin, one possible outcome is "Heads" (The Coat of Arms). Another possible outcome is "Tails". In the experiment of rolling a Ludo die, "rolling a 5" is one possible outcome. "Rolling a 2" is another. e. Sample Space (S) Definition: The sample space is the set of ALL possible outcomes of an experiment. Explanation: It's a complete list of everything that could possibly happen. We usually write it inside curly braces `{}`. Ghanaian Examples: Experiment: Tossing a 1 Cedi coin once. Sample Space (S): `{Heads, Tails}` Experiment: Rolling a standard six-sided Ludo die. Sample Space (S): `{1, 2, 3, 4, 5, 6}` Experiment: Checking the result of a football match between Hearts of Oak and Asante Kotoko. Sample Space (S): `{Hearts Win, Kotoko Win, Draw}` f. Event (E) Definition: An event is a specific outcome or a set of outcomes that we are interested in. It is a subset of the sample space. Explanation: An event is the "result we are looking for." It can be a single outcome (a simple event) or a group of outcomes (a compound event). Example using the Ludo Die Experiment: Sample Space (S): `{1, 2, 3, 4, 5, 6}` Event A: Getting a 6 (to start the game). This is a simple event. The set of outcomes for this event is E = `{6}`. Event B: Getting an even number. This is a compound event because multiple outcomes match. The set of outcomes for this event is E = `{2, 4, 6}`. Event C: Getting a number less than 3. This is a compound event. The set of outcomes for this event is E = `{1, 2}`.
Guided Practice (With Solutions)
Instructions: In your groups, discuss the following scenarios. Identify the experiment, list all possible outcomes, write down the sample space, and define the specified event.
Question 1: A bowl contains three different fruits: a mango, an orange, and a banana. You close your eyes and pick one fruit. a) What is the experiment? b) What are the possible outcomes? c) Write down the sample space, S. d) What are the outcomes in the event E, "picking a citrus fruit"?