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Video status: Related supplementary video included; the original lecture recording has not been verified. Source details
This is article 3 in Reading Stanford CS109, covering Stanford CS109, Summer 2026, Lecture 2 (Jun 23). The canonical schedule title is Conditional Probability, taught by Chris Gregg. This guide cross-checks the official schedule, lecture page, worksheet, answer key, and LLM guide. The lecture page and the /spr26 reader are shared, Spring-dated concept references.
Material fidelity is L3: the Summer schedule and problem artifacts establish the agenda; shared Spring-dated pages support concepts only. The Canvas recording was not used.
Worksheet agenda: conditioning, chain rule, total probability, and Bayes
The opening die problem reviews sets so that the numerator P(E∩F) has a concrete meaning. The second problem then compares three dice questions. Unconditionally, five ordered pairs sum to eight. Given that the first die is five, only six outcomes remain and only a second die of three succeeds. Given that at least one die is five, eleven outcomes remain and both (5,3) and (3,5) succeed. Similar English conditions produce different answers because they retain different sample spaces.
Drawing without replacement makes the chain rule visible. Two aces have probability 4/52 times 3/51. A king followed by a queen is 4/52 times 4/51. Three hearts multiply 13/52, 12/51, and 11/50. Every draw changes the next denominator and favorable count; that update is the dependence.
The spam problems form one probability tree. The prior is P(spam)=0.3 and the likelihood is P(free|spam)=0.6; the ham branch contributes 0.7 and 0.1. Total probability adds the two paths to “free,” giving 0.25. Bayes divides the spam-and-free path, 0.18, by that evidence to obtain posterior 0.72. Prior, likelihood, evidence, and posterior have distinct roles.
The medical-test problem exposes the base-rate effect. Among one thousand representative people, about ten have the disease and 9.8 test positive; among 990 healthy people, about 49.5 false positives appear. Most positive tests can therefore come from the much larger healthy group. High sensitivity is not high positive predictive value unless prevalence enters the denominator.
One tree unifies four formulas
Multiplying along branches is the chain rule. Adding disjoint paths to one label is total probability. After observing the label, asking which upstream branch produced it is Bayes. Mapping equations back onto this tree is more reliable than memorizing isolated fractions.
Material gaps
- The shared Spring-dated conditioning page supports the formulas and Bayes vocabulary, but not the Summer classroom sequence.
- recordings are Canvas-gated and were not used.
- This article does not use search snippets or inaccessible Canvas material, and it does not invent classroom examples.
Course video sources
Verified the official Summer 2026 archive: the course is recorded and its syllabus says recordings are available through Canvas. The archived homepage's Videos link redirects to Stanford Canvas login and requires course access, so there is no public Summer 2026 player. The 2022 Stanford Online public recording(s) below cover the same topic but come from a different offering with different lecture numbering; they are supplementary material, not Summer 2026 lecture recordings.
Original videos: Stanford CS109 I Conditional Probability and Bayes I 2022 I Lecture 4
Official sources:
- CS109 Summer 2026 — Canvas lecture recordings (login required)
- CS109 Summer 2026 — archived official schedule
- CS109 Summer 2026 — archived syllabus and recording policy
- Stanford Online CS109 2022 public playlist (different offering, supplementary)
Checked: 2026-10-10.
Content check: verified against the video transcript (2026-10-10): Read the transcript of 2022 Lecture 4, "Conditional Probability and Bayes" (Chris Piech, about 75 minutes): it covers conditional probability, the chain rule, the law of total probability and Bayes, matching this lecture's topic. The worksheet sections come from the Summer 2026 official problems, not from the video.
Update Log
- 2026-10-10: Added explicit video status and checked recording sources and access notes.
- 2026-10-10: Rechecked video status. Switched to related supplementary video: embedded the 2022 Stanford Online public recording on the same topic; the Summer 2026 original is behind Canvas sign-in and could not be verified.
- 2026-10-10: Checked the video content against its transcript. The video topic matches; no claims needed changing.
References
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