2.3StatisticsStretch

Conditional Probabilities in Venn Diagrams

A Venn diagram makes conditional probability concrete. To find P(A | B) you restrict to the part of the diagram inside B, then look at how much of it is also in A.

24 min Video by Zeeshan Zamurred Conditional Probability

Edexcel A level Maths: 2.3 Conditional Probabilities In Venn DiagramsWatch the full walkthrough before the notes below.

Open on YouTube

What you'll be able to do

Read probabilities from a Venn diagram
Compute conditional probabilities from regions
Fill in missing regions
Combine with the conditional formula

Reading conditional probabilities

To find $P (A ∣ B)$ , take the probability in $A \cap B$ and divide by the total probability inside $B$ . The diagram supplies both numbers directly.

P (A ∣ B) = \frac{P ( A \cap B )}{P ( B )} = \frac{overlap}{all of B}

Restrict to B, then look at the overlap.

\frac{0.15}{0.4}

= 0.375

Answer

0.375

Tip — The denominator is the TOTAL probability in B, including the overlap.

Completing the diagram

All regions (including outside both sets) must sum to 1. Use this to find a missing region before computing probabilities.

Formula recap

P (A ∣ B) = \frac{P ( A \cap B )}{P ( B )}

From the diagram.

all regions sum to 1

Completing the diagram.

Common mistakes to avoid

Using only the “A only” region as the numerator.

The numerator is the overlap A∩B.

Dividing by the overlap instead of all of B.

Denominator is the total inside B.

Key takeaways

P(A | B) = (A∩B) / (all of B).
Numerator is the overlap; denominator is everything in B.
All regions sum to 1 — use this to find a missing one.

Test yourself

Ready to lock in Conditional Probabilities in Venn Diagrams? Pick a mode and earn XP & Dobloons.