Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 10 chapters and video availability01 · Read and understand
What you will learn
- Calculate a conditional relative frequency from a two-way count table.
- Justify the method and check its domain, units, or logical conditions.
Before you start
Algebraic equations, ratios, angle and area facts, and basic coordinate geometry.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
Of 40 club members, 18 of 24 juniors and 8 of 16 seniors prefer morning meetings. What fraction of seniors prefer mornings?
Why this math matters
State the reference population whenever reporting a subgroup percentage. The example connects a stated condition to a conclusion and then checks whether the result satisfies that condition.
Set up the model
A useful answer starts with clear assumptions:
- Use the real-number system and the restrictions or data model stated in the question unless another domain is specified.
- Treat provided measurements as exact classroom-model values unless an approximation or uncertainty is stated.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Change the denominator when a condition is given
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Of 40 club members, 18 of 24 juniors and 8 of 16 seniors prefer morning meetings. What fraction of seniors prefer mornings?
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the conditions
Condition: restrict to the 16 seniors
The condition changes the reference group from all members to one subgroup.
Develop the calculation
8 morning-preferring seniors out of 16 seniors
Both numerator and denominator must follow the condition.
Check and interpret
8/16=1/2=50%
The overall morning fraction 26/40 answers a different question.
The result
8/16=1/2=50%
The overall morning fraction 26/40 answers a different question.
Common mistakes to catch
- Read the condition before choosing a denominator.
- P(A given B) generally differs from P(B given A).
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
What fraction of morning-preferring members are seniors?
Show a hint
Now restrict the denominator to all morning preferences.
Reveal answer and explanation
8/26=4/13
Reversing the condition changes the denominator, so the conditional proportions need not match.
Practice 2
Are grade group and morning preference independent in this table?
Show a hint
Compare the subgroup morning rates.
Reveal answer and explanation
No
Juniors have rate 18/24=75%, while seniors have 50%; the conditional rates differ.
Take the idea with you
State the reference population whenever reporting a subgroup percentage.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: A larger sample can still miss the population
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