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 7 chapters and video availability01 · Read and understand
What you will learn
- Explain how to list compound outcomes before counting.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Simple probability and even numbers.
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
Flip a fair coin and independently roll a fair four-sided die labeled 1 to 4. What is the probability of heads and an even number?
Why this math matters
A systematic outcome table prevents missing or duplicating possibilities in a two-stage experiment. Draw a tree or table when a multistage probability feels ambiguous.
Set up the model
A useful answer starts with clear assumptions:
- The coin and die are fair.
- The two outcomes are independent.
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.
List compound outcomes before counting
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Flip a fair coin and independently roll a fair four-sided die labeled 1 to 4. What is the probability of heads and an even number?
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 quantities
2 coin outcomes × 4 die outcomes = 8 outcomes
Independence and fairness make the eight ordered pairs equally likely.
Apply the relationship
favourable pairs: (H,2), (H,4)
Both conditions must hold in a pair.
Check and interpret
P(heads and even) = 2/8 = 1/4
The table agrees with multiplying 1/2 by 1/2.
The result
P(heads and even) = 2/8 = 1/4
The table agrees with multiplying 1/2 by 1/2.
Common mistakes to catch
- Exactly one head excludes two heads.
- Compound outcomes must remain ordered when stages are distinguishable.
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
With the same coin and die, find P(tails and a number greater than 1).
Show a hint
Count (T,2), (T,3), and (T,4).
Reveal answer and explanation
3/8
Three of the eight equally likely pairs satisfy both conditions.
Practice 2
For two independent fair coin flips, find P(exactly one head).
Show a hint
Write all four ordered outcomes.
Reveal answer and explanation
1/2
HT and TH qualify; HH and TT do not, so 2/4 = 1/2.
Take the idea with you
Draw a tree or table when a multistage probability feels ambiguous.
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: Recognize who a survey leaves out
Completion is your own study record, not a test score. It stays in this browser, does not sync to another device, and can be removed by clearing browser data.