Interpret probability and find the complementary event
Express probability as a fraction, decimal or percentage · Check the range from 0 to 1 · Use the complement to describe the event not occurring
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Equivalent fractions and percentages
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Express probability as a fraction, decimal or percentage
- Check the range from 0 to 1
- Use the complement to describe the event not occurring
A model of uncertainty
Probability describes how likely an event is under a stated model. Its value lies from 0 to 1 inclusive: 0% to 100%. A probability of 3/4 is 0.75 or 75%, not 3%. In a finite model whose possible outcomes all have positive probabilities, 0 represents an impossible event and 1 a certain event within that model.
A value greater than 1 or less than 0 is not a probability. A high probability is not a promise that the next trial succeeds; distinguish the model from what actually happens in a single trial.
Cover every other outcome
The complement of an event is all outcomes in the same sample space for which that event does not occur. Its probability is 1 minus the original probability. If the probability of rain is 0.35, the probability of no rain is 0.65. “Not red” includes every non-red category, not just blue.
Sources for this lesson
Pause and explain
If P(success)=0.72, is P(not success)=0.28?
Worked example
A bag has 3 red, 2 blue and 5 green counters, sampled uniformly. Find P(red) and P(not red).
Show the worked solution
- There are 10 equally likely individual counters.
- P(red)=3/10; the other 7 counters are non-red.
Answer P(red)=0.3=30%; P(not red)=0.7=70%.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A model gives P(late)=2/5. Express it as a decimal and percentage, then find P(not late).
Give me a hint
Convert the fraction, then subtract from 1.
Compare my reasoning
- 2/5=0.4=40%.
- The complement is 3/5=0.6=60%.
Late: 0.4 or 40%; not late: 3/5, 0.6 or 60%.
Look for these in your work
- Use equivalent representations
- Include all non-late outcomes
A bag has 4 red, 3 blue and 5 yellow counters. Find P(not red) for a uniform single draw.
Give me a hint
Count both non-red colours.
Compare my reasoning
- There are 12 counters and 8 are non-red.
- 8/12=2/3.
2/3.
Look for these in your work
- Use the total number of counters
- Include blue and yellow
A forecast gives a 10% chance of rain. A student says rain is impossible tomorrow. Evaluate this claim and find the chance of no rain.
Give me a hint
A probability of 0.1 is positive.
Compare my reasoning
- Rain is unlikely, but the model permits it.
- No rain has probability 1−0.1=0.9.
The claim is false; no rain has probability 90%.
Look for these in your work
- Separate likelihood from certainty
- Use the complementary event
Common mistakes
- Use the same sample space for an event and its complement.
- Do not confuse unlikely with impossible.
What can you explain now?
If P(success)=0.72, is P(not success)=0.28?
Compare with the explanation
Yes; the complementary probabilities sum to 1.
Every outcome is either success or not success within the stated model.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
If P(success)=0.72, is P(not success)=0.28?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.