SHS1 Mathematics · Semester 2, Week 18
Probability/chance
Lesson notes
Learning Objectives
Indicator: 1.4.2.LI.1 - List the elements of the sample space from a simple or compound experiment involving two independent events.
By the end of the lesson, learners can:
- Define sample space, experiment, trial, event, and independent events using their own words with at least one example for each term.
- List the elements of the sample space for a single experiment such as tossing one coin or rolling one die.
- Construct and list the complete sample space for a compound experiment involving two independent events, such as tossing two coins, rolling two dice, or tossing a coin and rolling a die.
- Use systematic listing methods, including tree diagrams and tables, to organise the outcomes of compound experiments.
- Determine whether two events are independent by checking whether the outcome of one does not affect the outcome of the other, and justify their reasoning.
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Sign in with phone numberCurriculum details
- Strand
- Making Sense of and Using Data (Strand 4)
- Sub-strand
- Probability/chance (4.2)
- Content standard
- 1.4.2.CS.1 - Demonstrate conceptual understanding of simple and compound probability experiments involving two independent events. 1.4.2.LO.1 Determine the sample space for simple and compound probability experiments involving independent events; express the probabilities of given events as fractions, decimals, percentages and/or ratios and solve problems everyday life problems.
- Indicator
- 1.4.2.LI.1 - List the elements of the sample space from a simple or compound experiment involving two independent events.
- Suggested placement
-
Semester 2, Week 18
(Week 38 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.
- Curriculum reference
- NaCCA curriculum document, p. 150
Exemplars (from the NaCCA curriculum)
Using think-pair square activities, learners engage in probability games to review compound probability and help reinforce understanding of the concepts (Hands-on probability games, QR Code Game, scavenger hunt, deal or no deal? Knockout Game) for the whole).
Using think-pair-share activities, discuss and write short notes (with examples) on the terminologies relating to the concept of probability. Example 1: i. Experiment ii. Random Experiment iii. Trial iv. Sample space v. Event vi. Equally Likely Events vii. Exhaustive Events viii. Favourable Events ix. Additive Law of Probability
Example 2: Discuss the concept of conditional probability as a prerequisite to understanding probability with independent events.
Example 3: Conditional probability P(A|B) is the probability of event A given the information that B has already taken place. For any two events A and B, P(A|B) is given as
P(A|B) = (P(A∩B))/(P(B)).
Example 4: Perform independent experiments and list the sample space For instance, i. Two events, A and B, are independent if P(A∩B) = P(A) P(B).
Consider tossing a coin three times in a row. Since each of the throws is independent of the other two, we consider all 8 (= 23) possible outcomes as equiprobable and assign each the probability of 1/8. Here is the sample space of a sequence of three tosses: {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.
ii. A fair die is rolled twice. List the sample space for the experiment. Solution: Sample space for two dice (outcomes):
Teaching and Learning Resources: - Manipulative (dice, coins, spinners, playing cards, counters, digit cards), - Simple Probability Mazes (Printable & Digital), - Worksheets - Task Cards - YEAR TWO Assessment (1.4.2.AS.1). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall; Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning.