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3
np=12×0.25.
Class 11 · English Version · Mathematics
Data, probability and written reasoning
Use a binomial count model and explain expected value.
About this lesson and its coverage
Original Kidemy Class 11 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 variable counts successes in n independent trials with equal success probability p. Its expected value np is the long-run mean count across comparable repeated batches, not a promise for one batch. Its variance np(1−p) measures average squared deviation in the model.
Worked example
For n=10,p=0.3, expected count3 and variance2.1. Individual batches can have other counts; the constant-chance and independence assumptions matter.
- 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.
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2.25
np(1−p)=12×0.25×0.75.
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1/8
(1/2)^3.
Write in your own words. A guardian or teacher should review this response.
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Expected count is a model average over many batches; a single batch varies.
Explain the meaning of expectation.
Write in your own words. A guardian or teacher should review this response.
Show model answer and explanation
The success chance can change after each draw, violating equal probability and independence.
State the mechanism.
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Notebook challenge, sources and further study
Apply the idea
Set up a fictional count model and explain its mean, variability and assumptions.
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- Use the stated evidence or givens.
- Show reasoning rather than only a result.
- Review and explain one correction.
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