Chance = wanted ÷ all
A mela wheel has 10 equal parts. 4 parts are shaded. You spin it once. What is the chance it stops on shaded?
- A wheel with 10 equal parts. Parts 1 to 4 are shaded.
- Count the parts you want. Shaded: 4.
- Count all the parts: 10.
- Chance of shaded = 4/10 = 2/5.
The chance of shaded is 4 out of 10, which is 2/5.
The rule
Use this rule when all outcomes are equally likely. That means each outcome has the same chance.
P(E) = number of favourable outcomes ÷ total number of outcomes
- Outcome — one possible result. Each part of the wheel is one outcome.
- Event E — the thing you ask about, like "shaded".
- Favourable outcomes — the outcomes you want.
- P(E) — the probability of E. Probability means chance.
The book calls this the theoretical probability of E. Equal parts of the wheel give equal chances.
More questions, same wheel
| Question | Wanted parts | All parts | Chance |
|---|---|---|---|
| shaded | 1, 2, 3, 4 | 10 | 4/10 = 2/5 |
| not shaded | 5 to 10 | 10 | 6/10 = 3/5 |
| a multiple of 4 | 4, 8 | 10 | 2/10 = 1/5 |
A bag of marbles
A bag has 4 red, 7 white and 5 green marbles. They are the same size. You take one out without looking.
- All marbles: 4 + 7 + 5 = 16.
- P(red) = 4/16 = 1/4. P(white) = 7/16.
Each marble is one outcome. All marbles are equally likely. So count marbles, not colours.
A coin and a pack of cards have fixed counts too. A coin has two faces, head and tail. A pack has 52 cards, 26 red and 26 black.
Now try it. Pick a colour. Count the lit marbles.
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