BASIC VOCABULARY
Experiment
process with random results
Outcome
single possible result
Sample space
all possible outcomes (S)
Event (A)
set of one or more outcomes
PROBABILITY SCALE
Always: 0 ≤ P(A) ≤ 1
THEORETICAL P(A)
Formula
favourable / total outcomes
Die, P(>4)?
Favourable: {5,6} = 2
Total: 6
P = 2/6 = 1/3
EXPERIMENTAL P(A)
Formula
successes / total trials
50 flips, 28 heads:
P(heads) = 28/50 = 0.56
Law of Large Numbers:
More trials → experimental P gets closer to theoretical P
COMPLEMENTARY EVENTS
Complement
A' = "A does NOT happen"
P(rain) = 0.35:
P(no rain) = 1 − 0.35 = 0.65
THEORETICAL VS EXPERIMENTAL
Theoretical
logic, equally-likely outcomes
Experimental
actual results from trials
TREE DIAGRAMS
- Each branch = one outcome
- Multiply along a path (AND)
- Add between paths (OR)
- Total outcomes = product of choices
Coin + die: P(H and 3)?
P = 1/2 × 1/6 = 1/12
Total outcomes = 2×6 = 12
OUTCOME TABLES (TWO DICE)
Make 6×6 grid. Total = 36 outcomes
P(sum=7)? Pairs: (1,6)(2,5)(3,4)(4,3)(5,2)(6,1) = 6
P = 6/36 = 1/6
COUNTING OUTCOMES
Fundamental
n₁ × n₂ × n₃ … = total
3 shirts × 2 pants = 6 outfit choices
COMMON MISTAKES
- P(A) > 1 is impossible — recheck!
- List ALL outcomes systematically
- Two dice: 36 outcomes, not 12
- AND events: multiply probabilities
- OR events (mutually exclusive): add
- Forgetting the complement shortcut
AND / OR RULES
P(A AND B)
P(A) × P(B) [if independent]
P(A OR B)
P(A) + P(B) [if mutually excl.]
Mutually exclusive = can't both happen at once
(e.g. rolling a 3 AND a 5 on one die)
USEFUL COMPLEMENT CASES
- P(at least one) = 1 − P(none)
- P(at least two) = 1 − P(0 or 1)
- Use complement when "at least" appears