🌎 Real-World Hook: Have you ever played Ludo or snakes and ladders? Every roll of a dice is a probability event! Weather forecasts say "70% chance of rain" — that is probability. Insurance companies, doctors, sports analysts, and stock market traders all use probability every single day. Even when your phone shows "Do you want to see more of this?" — it is using probability to guess what you like! Probability is the science of measuring chance, and it is all around us.
Probability is measured on a scale from 0 (impossible) to 1 (certain).
A fair coin has two equally likely outcomes: Heads or Tails.
A fair die has 6 equally likely outcomes. Each has probability 1/6.
A tree diagram shows every possible outcome step by step.
3 red and 2 blue balls. P(Red) = 3/5 because 3 out of 5 are red.
A fair die is rolled once.
Find the probability of getting a 4.
P = favourable outcomes ÷ total outcomes
A coin is tossed 50 times.
Heads came 22 times. Find P(Heads).
Experimental P = event count ÷ total trials
Two coins are tossed together.
Find P(at least one head).
List all outcomes, then count the ones you want
| Word / Rule | What It Means |
|---|---|
| Probability | How likely an event is. Number from 0 to 1 |
| Random | Cannot predict exactly what will happen |
| Sample space (S) | Set of ALL possible outcomes |
| Event | One or more outcomes you care about |
| Outcome | One single result of an experiment |
| Equally likely | All outcomes have the same chance |
| Experimental P | Event count ÷ total trials (from doing it) |
| Theoretical P | Favourable ÷ total (from logic) |
| P = 0 | Impossible. Can never happen |
| P = 1 | Certain. Will always happen |
| Tree diagram | Shows all outcomes of multi-step experiments |
| Gambler's Fallacy | Wrong belief that past changes future chances |
1. Probability is measured on a scale from ________ to ________.
2. The set of all possible outcomes is called the ________.
3. Experimental P = times event happened ÷ ________.
4. If an event is certain, its probability = ________.
5. Each face of a fair die has probability ________.
1. Probability can be more than 1. ________
2. A fair coin has two equally likely outcomes. ________
3. If you get heads 5 times, tails is more likely next. ________
4. Sample space of a die = {1, 2, 3, 4, 5, 6}. ________
1. A bag has 4 red and 6 blue balls.
Find P(red ball).
2. A die is rolled 30 times. Number 6 came 8 times.
Find the experimental P(6).
1. P = 0 — (a) Even chance
2. P = 1/2 — (b) Impossible
3. P = 1 — (c) Less likely
4. P = 1/6 — (d) Certain
Draw a tree diagram for tossing one coin twice.
List all 4 outcomes.
💡 Compare: Theoretical P(6) = 1/6 ≈ 0.167. In 30 rolls, the experimental result differs — this is normal! As we roll more times, experimental probability gets closer to 1/6.
The 4 outcomes when a coin is tossed twice:
💡 P(exactly one head) = 2/4 = 1/2. P(both heads) = 1/4. P(at least one head) = 3/4.
A measure of how likely an event is. Scale from 0 to 1.
You cannot predict exactly what will happen.
The set of ALL possible outcomes. Die: {1,2,3,4,5,6}.
Times event happened ÷ total trials. Based on doing it.
Favourable outcomes ÷ total outcomes. Based on logic.
P = 0. It can never happen.
P = 1. It will always happen.
Wrong belief that past results change future chances. They don't!
All the key ideas about probability in one picture.