Statistics Foundation · Lesson 3.3
Conditional probability.
Conditional probability explains how uncertainty changes when information is known. This lesson develops the idea through restricted sample spaces, Venn diagrams, two-way tables, tree diagrams and diagnostic-style reasoning.
Lesson route
Learn probability after information is known.
This lesson is the turning point of Module 3. Instead of asking only “how likely is A?”, students now ask “how likely is A after we know B?”
0–10 min
Why probabilities change
Understand that probability can change when new information is known.
10–25 min
Restricted sample spaces
See conditional probability as probability calculated inside a smaller sample space.
25–45 min
Conditional notation
Learn what P(A | B) means and why the vertical bar means 'given'.
45–65 min
Deriving the formula
Derive P(A | B) = P(A ∩ B) / P(B) using event regions.
65–85 min
Two-way tables
Use rows, columns and totals to calculate conditional probabilities.
85–115 min
Tree diagrams and interpretation
Connect conditional probability to sequential reasoning and diagnostic-style examples.
Mastery checklist
Students should see conditional probability as a change of reference group.
Read P(A | B) correctly.
Identify the condition in a probability statement.
Explain B as the restricted sample space.
Derive P(A | B) = P(A ∩ B)/P(B).
Calculate conditional probability from counts.
Use two-way tables correctly.
Interpret conditional branches in a tree diagram.
Avoid confusing P(A | B) with P(B | A).