Probability summary

Key learning points

• $P(A\cup B)=P(A)+P(B)-P(A\cap B)$.
• Independent events: $P(A\cap B)=P(A)P(B)$.
• Conditional $P(A|B)=\frac{P(A\cap B)}{P(B)}$.
• Multiply along tree branches; add mutually exclusive paths.

Worked example 1 — Simple probability

Fair die. $P(\text{prime})$?

Working

Primes: 2, 3, 5.

Worked example 2 — Complement

If $P(A)=0.35$, find $P(A')$.

Working

Complementary probabilities sum to 1.

Worked example 3 — Independent events

Two fair coins. $P(\text{two heads})$?

Working

Multiply independent probabilities.

Worked example 4 — Conditional

$P(A)=0.6$, $P(A\cap B)=0.2$. Find $P(B|A)$.

Working

Divide the joint probability by $P(A)$.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.