SHS2 Mathematics · Semester 2 Week 20: Probability/chance

Lesson notes

Learning Objectives

Indicator: 2.4.2.LI.2 - Solve everyday life problems involving the probability of two independent events.

By the end of the lesson, learners can:

Distinguish between dependent events and independent events by examining whether the outcome of the first event affects the probability of the second.
Apply the multiplication rule for independent events, P(A and B) = P(A) × P(B), to calculate compound probabilities.
Solve real-life probability problems involving two independent events, such as tossing two coins or drawing from two separate containers.
Use tree diagrams to represent and calculate the probability of outcomes from two independent events.
Interpret probability results in everyday contexts and communicate conclusions clearly in words.

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Curriculum details

Strand: Making Sense of and Using Data (Strand 4)
Sub-strand: Probability/chance (4.2)
Content standard: 2.4.2.CS.1 - Demonstrate a conceptual understanding of simple and compound probability experiments involving two dependent events. 2.4.2.LO.1 Demonstrate a conceptual understanding of simple and compound probability experiments involving two dependent events.
Indicator: 2.4.2.LI.2 - Solve everyday life problems involving the probability of two independent events.
Suggested placement: Semester 2, Week 20 (Week 40 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:

exemplars - p.296: this exemplar sets a two-dimensional construct - a stacked fraction, an index or a column vector - which the text layer flattens into separate lines, so the parts are present but their vertical arrangement is lost; read the page
Curriculum reference: NaCCA curriculum document, p. 296

Exemplars (from the NaCCA curriculum)

Collaborative Learning: In convenient groups, task learners to identify situations where dependent events are possible and create and solve problems on them. Engage learners in a discussion on the need not to misuse ideas in probability in unacceptable ways.
Example 1: Entertainment centres A juggler has seven red, five green, and four blue balls. During his stunt, he accidentally drops a ball and doesn't pick it up. As he continues, another ball falls down. What is the probability that the first ball that was dropped is blue and the second ball is green?
Solution: As we know, the first ball is not replaced by the juggler. So, after dropping the first ball, he is left with 15 balls. 4 The probability that the first ball is blue or P(blue ball) = 16 5 The probability that the second ball is green or P(green ball) = 15 The probability that the first ball is blue and the second ball is green: P(blue than green) = P(blue) × P(green) 4 5 1 = 16 × 15 = 12 .
Teaching and Learning Resources:
- * Manipulative (dice, coins, spinners, playing cards, counters, digit cards), * Simple Probability Mazes (Printable & Digital), * Worksheets * Task Cards
- YEAR THREE
Assessment (2.4.2.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall; Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning.