Making Predictions… · SHS2 Additional Mathematics

Lesson notes

Learning Objectives

Indicator: 2.4.2.LI.1 - Use De Morgan’s law in set theory to establish the addition and multiplication laws of probability and apply them to solve real life problems.

By the end of the lesson, learners can:

State De Morgan’s laws for two events A and B in both set notation and probability notation.
Derive the addition law of probability, P(A ∪ B) = P(A) + P(B) − P(A ∩ B), using De Morgan’s law and the complement rule.
Derive the multiplication law of probability for independent events, P(A ∩ B) = P(A) × P(B), and use it alongside the addition law.
Apply the addition and multiplication laws of probability to solve real life problems involving two events from the same experiment.
Explain the meaning of the complement of a union, P(A ∪ B)′, using De Morgan’s law, and use it to calculate probabilities in practical situations.

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Curriculum details

Strand: Handling Data (Strand 4)
Sub-strand: Making Predictions with Data (4.2)
Content standard: 2.4.2.CS.1 - Apply the addition and multiplication laws and axioms of probability to solve real life problems. 2.4.2.LO.1 Solve problems using the axioms and the laws of probability. 2.4.2.LO.2 Solve real life problems using combination and permutation.
Indicator: 2.4.2.LI.1 - Use De Morgan's law in set theory to establish the addition and multiplication laws of probability and apply them to solve real life problems.
Suggested placement: Semester 2, Week 16 (Week 36 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
Source document note: The official curriculum document has a fault in this entry, so the curriculum text above is transcribed exactly as printed:

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Curriculum reference: NaCCA curriculum document, p. 422

Exemplars (from the NaCCA curriculum)

Group work, Talk for Learning, and Building on what others say.
Learning Experience: Learners in groups discuss De Morgan's law and use it to solve problems.
Activity 1 Learners in groups give real life examples of independent variables in an experiment and debate on the probability of their occurrence. Learners extend the discussion to De Morgan's law in relation to two independent events, 𝐴 and 𝐵 from the same experiment. Mathematically, the probability of independent variables occurring as 𝐴 or 𝐵 or both is given by 𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 ∪ 𝐵)
Example 1 Two events 𝑅, and 𝑄 are such that (𝑅 ∪ 𝑄) = , 𝑃(𝑅) = 0.6 and 𝑃(𝑅 ∩ 𝑄) = 0.5. Find 𝑃(𝑄). )" "(
Solution 𝑃(𝑅 ∪ 𝑄) = 𝑃(𝑅) + 𝑃(𝑄) − 𝑃(𝑅 ∩ 𝑄) 23 = 0.6 + 𝑃(𝑄) − 0.5 30 2 𝑃(𝑄) = 3
Teaching and Learning Resources:
- Real-life data samples from both the school community and/or outside the school community.
- ICT tools
Assessment (2.4.2.AS.1). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding.