One step, one question
A simple event involves one action: one die roll, one card drawn, one spinner spin.
P(event) = number of favourable outcomes ÷ total number of outcomes
(when outcomes are equally likely)
The probability scale
| Probability | Meaning |
|---|---|
| 0 | impossible |
| close to 0 | unlikely |
| 0.5 | even chance |
| close to 1 | likely |
| 1 | certain |
A probability can never be less than 0 or more than 1.
Writing probabilities
The same probability can be written three ways:
- Fraction: 1/4
- Decimal: 0.25
- Percent: 25%
Examples
Spinner with 5 equal sections: red, red, blue, green, yellow.
- P(red) = 2/5 = 0.4 = 40%
- P(blue) = 1/5
- P(purple) = 0 (impossible)
Bag with 3 apples, 5 oranges, 2 pears.
- P(orange) = 5/10 = 1/2
- P(apple or pear) = 5/10 = 1/2
Class draw: 28 students, 1 name drawn. P(you) = 1/28.
The complement
P(not A) = 1 − P(A).
- P(not red) on the spinner = 1 − 2/5 = 3/5
All the probabilities of the separate outcomes add up to 1.
Unequal areas
On a spinner where red takes up 180°, blue 90° and green 90°:
- P(red) = 180/360 = 1/2
- P(blue) = 1/4
Use area or angle when sections aren’t equal.
Probability and fairness
A game is fair if each player has the same probability of winning. Rolling a die where Player A wins on 1–2 and Player B wins on 3–6 is not fair: A has 1/3, B has 2/3.
Worked examples
Example 1: P(rolling a prime) on a die?
Primes: 2, 3, 5 → 3/6 = 1/2.
Example 2: A bag has 7 blue and 3 white counters. P(white)?
3/10.
Example 3: P(drawing a vowel) from the letters of CANADA?
A, A, A → 3/6 = 1/2.
Common mistakes
- Counting favourable outcomes wrong (forgetting repeated letters or colours).
- Writing the probability as a ratio of favourable to unfavourable (3:7 instead of 3/10).
- Assuming equal chances on unequal spinners.
Try it yourself
- P(rolling a number greater than 4)?
- A bag has 2 red, 3 green, 5 blue marbles. P(green)?
- P(not green) for question 2?
- Is a game fair if A wins on heads and B wins on tails?
Answers: 1) 1/3 2) 3/10 3) 7/10 4) yes
Quick recap
- For a simple event, P = favourable outcomes ÷ total outcomes.
- Probability goes from 0 (impossible) to 1 (certain).
- P(not A) = 1 − P(A).