Probability
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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Geometric Distribution worksheets
Model the number of trials through the first success using exact, cumulative, tail, mean, and variance questions.
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Let X count trials through the first success, so X has support 1, 2, .... Assume independent trials with constant success probability and round only final probabilities.
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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 the trials-through-first-success convention consistently for geometric probabilities and moments.
Worked example
With p=1/4, find the probability that the first success occurs on trial 3.
(3/4)^2(1/4)=9/64.
Trials 1 and 2 must fail, and trial 3 must succeed.
Teaching notes
Make the practice count
- Write the counting convention beside X.
- For X>=k, require k-1 initial failures.
- Distinguish first success by k from first success exactly at k.
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