---
title: "Conditional Probability from Tables and Venn Diagrams"
description: "Work out the probability of one event given that another has happened, by restricting attention to the row, column or region the condition allows."
canonical: https://lightmysky.com/learn/mathematics/conditional-probability-from-tables-and-venn-diagrams-mt_Vx88ugViYP
source: https://lightmysky.com/learn/mathematics/conditional-probability-from-tables-and-venn-diagrams-mt_Vx88ugViYP.md
retrieved: 2026-09-12
---

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# 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.

Subject: Mathematics · Area: Probability · Ages 15 to 16
Page: https://lightmysky.com/learn/mathematics/conditional-probability-from-tables-and-venn-diagrams-mt_Vx88ugViYP

## Ready when they can

- 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)

## Lesson: Given that changes everything

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.

**Example.** 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.

**Tip.** 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.

**Recap.** Circle the given group first, then divide the overlap by that group alone.

## Practice

17 questions on this page, each with its working shown.

## Needs first

- [Sets & Venn Diagrams](https://lightmysky.com/learn/mathematics/sets-and-venn-diagrams-mt_1YwOCMMwD8)
- [Tree Diagrams Without Replacement](https://lightmysky.com/learn/mathematics/tree-diagrams-without-replacement-mt_NfiAY_wMwZ)
- [Two-Way Tables](https://lightmysky.com/learn/mathematics/two-way-tables-mt_oD1Rgg52n3)

## Opens up

- [Setting Up a Hypothesis Test](https://lightmysky.com/learn/mathematics/setting-up-a-hypothesis-test-mt_JmpLNHK0Nf)
- [Conditional Probability, Independence and Bayes' Theorem](https://lightmysky.com/learn/mathematics/conditional-probability-independence-and-bayes-theorem-mt_wIi_XRzwwK)