Probability Topic Review summary

Key learning points

• $0\\le P(A)\\le1$; $P(A')=1-P(A)$.
• Mutually exclusive: $P(A\\cup B)=P(A)+P(B)$.
• Independent: $P(A\\cap B)=P(A)P(B)$.
• General addition: $P(A\\cup B)=P(A)+P(B)-P(A\\cap B)$.
• Tree diagrams: multiply along branches; add distinct routes.

Worked example 1 — Independent

$P(A)=0.3$, $P(B)=0.5$ independent. $P(A\\cap B)$?

Working

Product rule.

Worked example 2 — Complement

$P(A)=0.82$. $P(A')$?

Working

$1-P(A)$.

Worked example 3 — 0\\\\le P(A)\\\\le1; P(A')=1-P(A)

$0\\\\le P(A)\\\\le1$; $P(A')=1-P(A)$.

Working

Attempt without notes, then check the answers PDF.

Worked example 4 — Mutually exclusive: P(A\\\\cup B)=P(A)+P(B

Mutually exclusive: $P(A\\\\cup B)=P(A)+P(B)$.

Working

Attempt without notes, then check the answers PDF.

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.