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When One Thing Changes Another: Probability & Statistics: Uncharted

Courses Probability & StatisticsWhen One Thing Changes Another

When One Thing Changes Another

Shrink the denominator honestly, follow probability trees, and update beliefs without reversing the question.

Probability & Statistics
Unit 4 of 12
20 lessons
159 min
420 XP

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Lessons

20 total

1The Question Behind GivenDistinguish a conditional probability from its reversed question.InteractiveConcept7 min20 XPOpen
2Shrink the WorldRepresent a given condition by restricting the sample-space denominator.InteractiveConcept8 min20 XPOpen
3Two-Way TablesRead a conditional probability from the appropriate row or column of counts.InteractiveConcept8 min20 XPOpen
4Fill the TableReconstruct the four interior counts of a two-way table from its margins.InteractiveConcept8 min20 XPOpen
5Table WorkoutRead conditional fractions from varied two-way count tables.InteractivePractice9 min20 XPOpen
6Independent or NotTest independence by asking whether a condition changes a probability.InteractiveConcept7 min20 XPOpen
7Grow a TreeBuild complementary branch probabilities that sum to one at every fork.InteractiveConcept8 min20 XPOpen
8Multiply Along the BranchesFind a complete path probability by multiplying its conditional branches.InteractiveConcept7 min20 XPOpen
9Add Across the LeavesAdd disjoint leaf probabilities that lead to the same final event.InteractiveConcept7 min20 XPOpen
10The Drawn Marble RemembersUpdate a second-draw probability after sampling without replacement.InteractiveConcept8 min20 XPOpen
11Tree WorkoutTranslate restricted groups into conditional fractions across fresh cases.InteractivePractice9 min20 XPOpen
12The Positive TestPredict how a rare base rate changes the meaning of a positive test.InteractiveConcept8 min20 XPOpen
13Count the ThousandCompute a posterior probability from natural-frequency counts.InteractiveConcept8 min20 XPOpen
14Bayes Without the FormulaBuild a natural-frequency display whose positive column reveals the posterior.InteractiveConcept9 min20 XPOpen
15Base Rates RuleSee how prevalence changes the posterior from the same test result.InteractiveConcept8 min20 XPOpen
16Spam Filter ThinkingCompare evidence by how differently it appears across competing explanations.InteractiveConcept7 min20 XPOpen
17Update AgainUse a second independent positive result to update an existing posterior.InteractiveConcept8 min20 XPOpen
18Conditional WorkoutRead and update conditional probabilities across fresh frequency tables.InteractivePractice9 min20 XPOpen
19Courtroom FallaciesReject the prosecutor's fallacy by keeping conditional directions distinct.InteractiveConcept7 min20 XPOpen
20Conditional Mastery CheckCombine a probability tree, natural frequencies, and a conditional table in one update.InteractiveMastery check9 min40 XPOpen

Counting Without Listing What to Expect