Probability
Discrete Probability Distributions worksheets
Use valid finite probability tables to find missing entries, event probabilities, expected value, and population variance.
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Total Probability and Bayes' Theorem worksheets
Practice forward total probability and reverse conditional probability with explicit two- and three-source partitions.
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Use the exhaustive, disjoint source branches. Show the total-event sum before any reverse conditional probability, then round only the final result.
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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
Use exhaustive disjoint branches to find a total event probability, then reverse the conditioning correctly with Bayes' theorem.
Worked example
Sources A and B supply 40% and 60% of items; their pass rates are 80% and 90%. Find P(A | pass).
0.40(0.80) / [0.40(0.80)+0.60(0.90)] = 0.372.
The denominator is the total pass probability across both disjoint sources.
Teaching notes
Make the practice count
- Label priors before conditional rates.
- Compute the total conditioning-event probability before the Bayes numerator.
- Check that posterior probabilities stay between 0 and 1.
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Choose two- or three-source partitions, forward or reverse probability, final precision, and question count.
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