The Language of Chance
The words on the scale: impossible (0) → unlikely → evens (½, an equal chance either way) → likely → certain (1).
For equally likely outcomes: probability = favourable outcomes ÷ total outcomes. A fair dice has 6 equally likely faces, so P(rolling a 4) = \(\dfrac{1}{6}\).
A fair coin is flipped. Where does “lands on heads” sit on the scale?
Two equal outcomes → P(heads) = \(\dfrac{1}{2}\) — exactly evens.
A bag holds 3 red and 7 blue counters. Find P(red).
3 favourable out of 10 total → P(red) = \(\dfrac{3}{10}\) = 0.3 = 30%.
A fair dice is rolled. Find P(number less than 7) and P(rolling a 9).
Every face is less than 7 → P = 1 (certain). No face shows 9 → P = 0 (impossible).
Which is more likely: rolling an even number on a dice, or picking a red counter from Example 2’s bag?
P(even) = \(\dfrac{3}{6}\) = 0.5; P(red) = 0.3. The even number — compare by converting to decimals.
Q1. A fair dice is rolled. Find P(rolling a 2).
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Q2. A bag has 4 green and 6 yellow sweets. Find P(green) as a decimal.
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Q3. Which word describes an event with probability 0.9?
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Q4. A spinner has 8 equal sections: 5 blue, 2 red, 1 white. Find P(blue) and P(not white).
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P(not white) = 78 ✓ B1
Q5. Tebogo says the probability of rain tomorrow is 1.4. Explain why he must be wrong.
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- Writing probabilities as ratios (“3 : 10”) — use a fraction, decimal or percentage.
- Counting colours instead of counters: a bag of 3 red and 7 blue has 10 outcomes, not 2.
- Probabilities above 1 or below 0 — always impossible.
- Assuming outcomes are equally likely when they are not (a bent coin, an unfair spinner).
Paper 1 and 3 open with 1-mark probability reads exactly like these. Core sharpens the tools next: the complement rule and expected frequency in P-C1 and P-C2.