Chance Encounters
Put a number on chance: place events on the 0–1 scale, calculate theoretical probabilities, use "everything sums to 1", and turn probability into expected frequency for real experiments.
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Chance Encounters 🎲
Probability turns "probably", "unlikely" and "fifty-fifty" into **numbers** you can calculate with. Every probability sits on a scale from **0** (impossible) to **1** (certain). Master a few rules here — the scale, the counting formula, and "everything sums to 1" — and most of the probability paper is yours.
The 0 to 1 scale 📏
A probability is always between **0 and 1**: • **0** = impossible, **1** = certain, **0.5** = an even chance. • The closer to 1, the more likely; the closer to 0, the less likely. ⚠️ Write probabilities as **fractions, decimals or percentages** — never as a **ratio** like 3 : 5. A ratio scores no marks for a probability.
Match the word to its probability
- Impossible
- Certain
- Even chance
- Unlikely
- 0
- 1
- 0.5
- 0.2
Theoretical probability 🧮
When outcomes are **equally likely**, you can calculate the probability by counting: **P(event) = favourable outcomes ÷ total outcomes.** A fair six-sided die has 6 equally likely outcomes. Three of them are even (2, 4, 6), so P(even) = 3 ÷ 6 = 1/2 = **0.5**.
Spin the spinner
An interactive activity.
Everything sums to 1 ➕
The probabilities of **all** possible outcomes always add up to **1**. That gives a powerful shortcut for "not" questions: **P(not A) = 1 − P(A).** If the probability it rains tomorrow is 0.3, then the probability it does NOT rain is 1 − 0.3 = **0.7**.
The complement
An interactive activity.
Mutually exclusive events
A bag holds red, blue and green counters. P(red) = 0.4 and P(blue) = 0.35. A counter cannot be two colours at once, so what is P(red OR blue)?
- 0.75
- 0.14
- 0.05
- 0.25
Experiments and expected frequency 📊
Sometimes outcomes are not equally likely (a bent coin, a drawing pin), so you **experiment** and use **relative frequency = frequency ÷ number of trials** as an estimate. Turn a probability into a prediction with **expected frequency = probability × number of trials**. For P = 0.2 over 50 trials, you expect 0.2 × 50 = **10** successes.
Expected frequency
An interactive activity.
Which estimate is more reliable?
Ann throws a drawing pin 20 times to estimate P(point up); Ben throws it 500 times. Whose relative frequency is likely to be the more reliable estimate?
- Ben — more trials means the relative frequency is closer to the true probability
- Ann — fewer throws gives a cleaner result
- They are equally reliable
- Neither can be used as an estimate
Probability rules
On the probability scale, an impossible event has probability _____ and a certain event has probability 1. Because all outcomes sum to 1, the probability an event does NOT happen is found by _____ the probability it does from 1. To predict results, expected frequency = probability _____ the number of trials.