Week 4 · Suggested 75 minutes · First-pass draft
How many ways could the event occur?
Connect enumeration, mutually exclusive events, independent trials, and conditional probabilities.
Applied assignment, not a stored grade. Instructions and model checks are provided for self-study or instructor adaptation. Work is not transmitted to this site.
What you will do
- Enumerate the sample space for three fair coin tosses and identify the event containing at least two heads.
- Compute the probability of that event by counting and then by a binomial formula.
- Construct a two-branch probability tree for the fictional transit/early-commute example from the lesson.
- Explain why independence and mutual exclusivity are not synonyms using one counterexample.
What to submit
A complete enumeration, one probability tree, two independent calculations, and a statement of assumptions.
Self-check before finishing
At least two heads in three fair tosses has probability 4/8=1/2.
Assigned reading
Count outcomes and compute conditional probabilities under explicit models.
- Lesson 12: probability as model
- Lesson 13: counting and combinations
- Lesson 14: conditional independence and trees
Instructor discussion guidance
Demand clear denominators for conditional probabilities and an explicit equal-likelihood model when using counting.
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