Conditional Probability from Tables and Venn Diagrams
Work out the probability of one event given that another has happened, by restricting attention to the row, column or region the condition allows.
What a learner can do afterwards
- Read a conditional probability from a two-way table using the row total as the denominator
- Find a conditional probability from a region of a Venn diagram
- Explain in words how P(A given B) differs from P(B given A)
1 · Read
A conditional probability zooms into one subgroup. The words after GIVEN name the denominator: only those cases count. P(tennis given girl) uses the girls alone, never the whole school.
120 girls, and 30 of them play tennis. Restrict to the girls row: 30 over 120 = 0.25. From a table, a conditional is one cell over its row or column total. Reading the other way, 30 girls out of 50 tennis players gives P(girl given tennis player) = 30 over 50 = 0.6.
Venn regions show the same zoom. With A-only 12, both 8, B-only 20, circle B first: it holds 28, so P(A given B) = 8 over 28 = 2 over 7. The reverse uses the other circle: P(B given A) = 8 over 20 = 0.4. Same overlap, different denominator, different answer.
P(A given B) and P(B given A) answer different questions, so read the GIVEN part carefully every time. Mixing them up is the classic fallacy behind misleading test scares: a rare condition makes most positives false alarms. Direction matters.
Circle the given group first, then divide the overlap by that group alone.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.