Examples and practice
Probability and conditional information
Back to lessonPractice section 1 · Questions 1–6
Compare the two opening dice events · Can one match have two incompatible goal totals? · +4 more
Practice section 2 · Questions 7–12
Distinguish dependence from a nonempty overlap · Find P(A) before testing independence · +4 more
Practice section 3 · Questions 13–18
Distinguish separated Es from not all Es together · Arrange PROBABILITY with adjacent or separated Is · +4 more
Practice section 4 · Questions 19–24
Use order counts instead of expanding every draw path · Sum the chances of winning on successive rounds · +4 more
- Use order counts instead of expanding every draw path
- Sum the chances of winning on successive rounds
- Find the least dart count for a strict probability target
- Two throws: ordered outcomes and conditioning
- Recover a marginal probability from a conditional one
- Use the same equally likely four-person selections throughout
Practice section 5 · Questions 25–30
Distinguish not-all-together from pairwise separation · Use base rates before interpreting a positive result · +4 more
- Distinguish not-all-together from pairwise separation
- Use base rates before interpreting a positive result
- Use overlap bounds before adding the conditional information
- Sum mutually exclusive winning rounds as a geometric series
- Differentiate the posterior probability over its percentage domain
- Solve for a parameter and enforce probability bounds
Practice section 6 · Questions 31–36
Recover the marginal before testing independence · Link both conditional probabilities through the shared intersection · +4 more
- Recover the marginal before testing independence
- Link both conditional probabilities through the shared intersection
- Bound the part of C lying in B but outside A
- Recover A from a disjoint region before using independence
- Keep the two dice ordered when checking event independence
- Account for the first red ball being removed
Practice section 7 · Questions 37–42
Use the preceding meal to choose each transition probability · Condition a hypergeometric count on at least one match · +4 more
- Use the preceding meal to choose each transition probability
- Condition a hypergeometric count on at least one match
- Keep a grouped IP pair and separately place the JC2 members
- Condition on the first black draw before counting the remaining whites
- Separate dependent sets from independent repeated matches
- Give proper fractions and condition on both people finding jobs
Practice section 8 · Questions 43–45
Distinguish finite sampling from independent-person conditioning · Correct the intermediate expansion before solving for the percentage · +1 more