Conditional Probability (Extended)
Understand P(A|B), two-way tables and conditional probability in real contexts. IB MYP Year 5 Extended Maths — clear formula, worked logic and common errors.
Probability Given Known Information
Conditional probability is the probability of event A occurring given that event B has already occurred. This changes the sample space we are working within and is one of the most conceptually important ideas in Extended probability.
The Conditional Probability Formula
P(A | B) = P(A and B) / P(B)
Read P(A | B) as "the probability of A given B." You are restricting your attention to the outcomes where B has occurred and asking how many of those also include A.
Two-Way Tables
Two-way (contingency) tables are a highly effective tool for conditional probability. They display frequencies (or probabilities) for two categorical variables and make it straightforward to read off conditional values.
When using a two-way table:
- Identify the condition — this determines which row or column you restrict to
- Find the total for that row or column
- Identify how many entries in that row or column satisfy event A
- Divide to find P(A | B)
Conditional Probability in Real Contexts
MYP Criterion D tasks frequently frame conditional probability in scenarios such as:
- Medical testing (probability of having a condition given a positive test result)
- Survey data (probability of preferring a product given a particular age group)
- Quality control (probability of a defect given a specific production line)
Common Mistakes
- Reversing the condition: P(A | B) ≠ P(B | A) in general
- Using the full sample space instead of the restricted one after a condition is stated
- Misreading two-way table totals (using row totals when column totals are needed)