IEB Grade 11 Probability Cheat Sheet

Probability is about 20 marks of Grade 11 Paper 1. Every rule and method is here.

Rules

• $P(E)=\frac{n(E)}{n(S)}$ for equally likely outcomes.

• $P(A\text{ or }B)=P(A)+P(B)-P(A\text{ and }B)$

• Mutually exclusive: $P(A\text{ and }B)=0$. Complement: $P(\text{not }A)=1-P(A)$.

• Independent: $P(A\text{ and }B)=P(A)\times P(B)$; use it as the test.

• Mutually exclusive events (with non-zero probabilities) are never independent.

Venn diagrams

• Fill from the inside out: all three, then exactly two, then 'only', then outside.

• Unknown region: write every region in terms of $x$ and use the total.

Tree diagrams

• Multiply along a path; add separate paths.

• Without replacement: the numbers on later branches change.

• 'At least one' = $1-P(\text{none})$.

Contingency tables

• Complete the totals first. Divide by the grand total.

• Independence test: compare $P(A)\times P(B)$ with $P(A\text{ and }B)$, then conclude in words.

Know by heart

• The addition rule

• The independence test

• Inside-out Venn filling

On the formula sheet

• $P(A)=\frac{n(A)}{n(S)}$

• $P(A\text{ or }B)=P(A)+P(B)-P(A\text{ and }B)$

Common traps

• Confusing independent with mutually exclusive.

• Keeping the same denominator without replacement.

• Entering given totals as 'only' regions in a Venn diagram.

Related topics

• probability rules
• independent and dependent events
• venn diagrams
• tree diagrams
• contingency tables