Describe outcomes and “or”, “and” and “not” events
List a complete sample space without duplicates · Describe events as groups of outcomes · Distinguish inclusive or, intersection and complement in words
Section Paper 2 · Historical Extended · non-calculator
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
- Divisibility and simple counting
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
- List a complete sample space without duplicates
- Describe events as groups of outcomes
- Distinguish inclusive or, intersection and complement in words
Outcomes before categories
A sample space is the complete collection of possible outcomes of the experiment. For one fair six-sided die it is 1,2,3,4,5,6. Each face has probability 1/6. The event “even” contains 2,4,6, so its probability is 3/6. Counting favourable outcomes divided by all outcomes works only when those individual outcomes are equally likely.
Three colour names do not make their probabilities 1/3 if there are different numbers of counters of each colour. Choose a sample space at a level that justifies the weights.
Use words to combine events
For a die let A mean even and B mean greater than 4. “A and B” means both descriptions hold, giving 6 only. “A or B” is inclusive: either or both hold, giving 2,4,5,6, with 6 counted once. “Not A” gives 1,3,5. Formal set notation is not expected for these 0444 requirements.
Sources for this lesson
Pause and explain
Does “even and greater than 4” contain 4?
Worked example
For a fair die, find the probability of even or greater than 4.
Show the worked solution
- List the event: 2,4,5,6.
- Four distinct faces out of six satisfy it.
Answer 4/6=2/3.
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.
For a fair die, list the odd outcomes and find P(odd).
Give me a hint
List the faces before counting.
Compare my reasoning
- Odd outcomes are 1,3,5.
- Three of six equally likely faces are favourable.
1,3,5; P(odd)=1/2.
Look for these in your work
- List distinct outcomes
- State the equal-likelihood assumption
For a fair die, find P(even and greater than 3), then P(even or greater than 3).
Give me a hint
The two lists are 2,4,6 and 4,5,6.
Compare my reasoning
- Both descriptions hold at 4 and 6: 2/6.
- Either description holds at 2,4,5,6: 4/6.
And: 1/3; or: 2/3.
Look for these in your work
- Require both for and
- Remove repeated outcomes for or
A bag contains 6 red and 2 blue counters. A student lists red and blue and concludes each has probability 1/2. Correct the model for a uniform draw.
Give me a hint
The counters, not the two colour names, are equally likely.
Compare my reasoning
- There are eight equally likely counters.
- Six are red and two blue.
P(red)=3/4; P(blue)=1/4.
Look for these in your work
- Identify equally likely individual outcomes
- Do not assign equal weights to unequal categories
Common mistakes
- Inclusive or allows both descriptions.
- A repeated outcome is counted once.
What can you explain now?
Does “even and greater than 4” contain 4?
Compare with the explanation
No; only 6 satisfies both descriptions.
The value 4 is even but is not greater than 4.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Does “even and greater than 4” contain 4?
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.