Mathslive.ie

PROBABILITY

Exam Cog
THE FORMULA

P(E) = desired ÷ total

0 = impossible   1 = certain

AND ×   OR +

SAMPLE SPACE

List every equally-likely outcome

2 coins = 4 · 3 coins = 8 · 2 dice = 36

★ A grid works well for two dice
COUNTING PRINCIPLE

Multiply the options at each stage

3 × 4 × 2 × 3 = 72

A fixed choice counts as 1.

TREE DIAGRAMS

Multiply ALONG a path

Add BETWEEN paths

“At least one” = add the paths that have it

RELATIVE FREQUENCY

= result ÷ trials

Estimates probability from real results

All rel. freqs add to 1

WATCH-OUTS
HHT, HTH, THH are three different outcomes — order matters when you list.