Show model answer and explanation
4
np=20×0.2.
A Level · English Medium · Cambridge · Mathematics
Data, probability and written reasoning
Use binomial and transformed-variable models with explained assumptions.
About this lesson and its coverage
Original Kidemy A Level progression. This level has its own text, examples and questions. Curriculum versions share the progression; complete board-specific coverage still needs specification matching and additional material.
Learn the idea
A binomial count uses independent trials with fixed success probability. Its mean np is the model’s repeated-batch average; variance np(1−p) is squared spread about that average. A transformation Y=aX+b changes variance by a², because deviations are scaled by a.
Worked example
For X~Bin(8,0.5), mean4 and variance2. If Y=3X+1, mean13 and variance18; this describes model averages and variability, not guaranteed outcomes.
- Identify the quantities and restrictions.
- Show a method with units or symbols.
- Check and explain the result.
Your written practice
Show your working on paper. Check your answer, then choose Next.
Show model answer and explanation
3.2
20×0.2×0.8.
Show model answer and explanation
12.8
4×3.2.
Write in your own words. A guardian or teacher should review this response.
Show model answer and explanation
C(4,1)(1/2)^4=4/16=1/4.
Count the possible head positions.
Write in your own words. A guardian or teacher should review this response.
Show model answer and explanation
The product probabilities rely on independence; dependence changes probabilities of count patterns.
Explain a mechanism such as linked outcomes.
Progress and browser storage
Notebook challenge, sources and further study
Apply the idea
Build a count model and a transformed score, interpreting mean and variance in context.
Review with a guardian or teacher
- Use the stated evidence or givens.
- Show reasoning rather than only a result.
- Review and explain one correction.
Keep your work on paper or in a local file. This page does not upload it or automatically grade the project.
Teacher-led lessons, schedules and prices for this outline are upcoming. You can use any starter practice above now without booking.
Your next step
Solo practice works without an account. Sign in to save a practice record to your learner profile.
Keep practising
Exact lesson links and related activities are labelled separately. Return-to-course links retain your selected learning path.