Probability
Binomial Distribution worksheets
Calculate exact, at-most, and at-least binomial probabilities plus mean and variance for bounded trial counts.
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Discrete Probability Distributions worksheets
Use valid finite probability tables to find missing entries, event probabilities, expected value, and population variance.
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Use the complete labeled probability table. Check that probabilities sum to 1, and show exact fraction work for events, expectation, and population variance.
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Each worksheet states the sample-space assumptions, distribution support, and counting convention needed for the selected model. Probability tables stay fully labeled, and Bayes questions identify the conditioning event before reversing it.
Learning objective
What this activity builds
Interpret a finite integer-valued distribution and calculate exact probabilities, expectation, and population variance.
Worked example
For x = 0,1,2 with probabilities 1/4, 1/2, 1/4, find E(X).
E(X) = 0(1/4)+1(1/2)+2(1/4)=1.
Expectation is the probability-weighted average of all support values.
Teaching notes
Make the practice count
- Verify the table totals 1 before calculating.
- Keep support values paired with their probabilities.
- Use E(X^2)-[E(X)]^2 for variance.
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