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0.3
0.18/0.6.
Class 12 · Bangla Version · Mathematics
Data, probability and written reasoning
Use conditional probabilities and transform a random variable’s mean and spread.
About this lesson and its coverage
Original Kidemy Class 12 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
Conditional probability changes the reference event: P(A|B)=P(A∩B)/P(B) when P(B)>0. If Y=aX+b, its mean becomes aE(X)+b and variance a²Var(X). Variance measures squared spread; adding a constant shifts location without changing spread.
Worked example
If E(X)=4 and Var(X)=9, then Y=2X+1 has mean9 and variance36. This describes a model’s average and squared variability, not an individual outcome.
- 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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13
3×5−2.
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36
3²×4.
Write in your own words. A guardian or teacher should review this response.
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The mean also rises by 7, so each deviation from the mean stays the same.
Explain deviation, not only quote a rule.
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There is no positive-probability reference group B to divide by.
State the denominator condition.
Progress and browser storage
Notebook challenge, sources and further study
Apply the idea
Create a two-way probability table and explain two conditional results.
Review with a guardian or teacher
- Use the stated evidence or givens.
- Show reasoning rather than only a result.
- Review and explain one correction.
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