SHS2 Mathematics · Semester 2 Week 19: Probability/chance

Lesson notes

Learning Objectives

Indicator: 2.4.2.LI.1 - List the elements of the sample space from a simple or compound experiment involving two dependent events.

By the end of the lesson, learners can:

Define dependent events and distinguish them from independent events using the criterion of whether the outcome of the first event affects the probability of the second event.
List all elements of the sample space for a compound experiment involving two dependent events, using organised listing methods such as tree diagrams or tables.
Apply the multiplication rule P(A and B) = P(A) × P(B after A) to calculate probabilities of compound outcomes when the first item is not replaced.
Use the step-by-step procedure to classify a given probability scenario as dependent or independent before solving it.
Work collaboratively in mixed-ability groups to present and justify sample spaces and probability calculations for real-life dependent event scenarios.

Sign in with your phone number to read the full note and download the GES plan - free.

Sign in with phone number

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.1 - List the elements of the sample space from a simple or compound experiment involving two dependent events.
Suggested placement: Semester 2, Week 19 (Week 39 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.294: 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. 294

Exemplars (from the NaCCA curriculum)

Using Talk for Learning: Engage learners to brainstorm and make presentations on the meaning of dependent events. Encourage learners to tolerate each other's views.
Example 1: Events are dependent if the outcome of one event affects the outcome of another. For instance, if you draw two colored balls from a bag and the first ball is not replaced before you draw the second ball, then the outcome of the second draw will be affected by the outcome of the first draw.
E.g. If A and B are dependent events, then the probability of A happening AND the probability of B happening, given A, is P(A) × P(B after A). P(A and B) = P(A) × P(B after A) P(B after A) can also be written as P(B | A) then P(A and B) = P(A) × P(B | A)
Example 2: A purse contains four GHC5 notes, five GHC10 notes and three GHC20 notes. Two notes are selected without the first selection being replaced. Find P(GHC5, then GHC5).
Solution: There are four GHC5 notes. There are a total of twelve notes. 4 P(GCH5) = . 12 The result of the first draw affected the probability of the second draw. There are three GHC5 notes left. There are a total of eleven notes left. 3 P(GHC5 after GHC5) = . 11 P(GHC5, then GHC5) = P(GHC5) · P(GHC5 after GHC5) 4 3 1 = 12 x 11 = 11 .
1 The probability of drawing a GHC5 bill and then a GHC5 bill is 11 .
Using think-pair-share activities, discuss the differences between dependent and independent probability events.
Example Dependent Events Independent Events 1. The occurrence of one event affecting the 1. The occurrence of one event not affecting probability of another event. the probability of another event. 2. Examples include a power cut in case you don't 2. Examples include riding a bike and pay your bill on time, winning the lottery after watching your favourite movie on a laptop buying 10 lottery tickets (the more tickets bought, the greater the chance of winning) 3. Formula can be written as: 3. Formula can be written as: P(A and B) = P(A) × P(B | A) P(A and B) = P(A) × P(B)
Using think-pair-share activities, discuss the steps in determining whether a probability is dependent or independent. As learners pair-share ideas, promote respect for divergent views to ensure inclusivity in the mathematics learning environment.
Example: Steps to Check Whether the Probability Belongs to Dependent or Independent Events
- Step 1: Is it possible for the events to happen in any order? If yes, go to step 2; if no, go to step 3.
- Step 2: Does one event affect the outcome of the other event? If yes, go to step 4; if no, go to step 3.
- Step 3: The event is independent. Simply put the formula of independent event and get the answer.
- Step 4: The event is dependent. Simply put the formula of the dependent event and get the answer.
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.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.