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Teaching video
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Grade 7 chapters and video availability01 · Read and understand
What you will learn
- Explain how to find a probability through its complement.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Fractions and counting equally likely outcomes.
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
A bag contains 5 green, 3 orange, and 2 purple counters. One counter is selected uniformly at random. Find the probability that it is not green.
Why this math matters
An event and its complement cover all possibilities without overlap, so their probabilities sum to one. Use the complement when the excluded outcomes are easier to count than the requested outcomes.
Set up the model
A useful answer starts with clear assumptions:
- Each individual counter is equally likely to be selected.
- The colours listed exhaust the contents of the bag.
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.
Find a probability through its complement
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A bag contains 5 green, 3 orange, and 2 purple counters. One counter is selected uniformly at random. Find the probability that it is not green.
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
total counters = 5 + 3 + 2 = 10
Use the count of all possible individual selections.
Apply the relationship
P(green) = 5/10 = 1/2
Five of the ten equally likely selections are green.
Check and interpret
P(not green) = 1 − 1/2 = 1/2
Orange and purple together contain the other five counters.
The result
P(not green) = 1 − 1/2 = 1/2
Orange and purple together contain the other five counters.
Common mistakes to catch
- Not green includes every other colour, not just one selected colour.
- A count ratio needs equally likely elementary outcomes.
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
An event has probability 0.27. Find its complement's probability.
Show a hint
Subtract from one.
Reveal answer and explanation
0.73
1 − 0.27 = 0.73.
Practice 2
For a fair six-sided die, find P(not greater than 4).
Show a hint
List the outcomes that fail to exceed 4.
Reveal answer and explanation
2/3
The outcomes are 1, 2, 3, 4: four of six equally likely outcomes.
Take the idea with you
Use the complement when the excluded outcomes are easier to count than the requested outcomes.
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: Separate observed frequency from certainty
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