Counting what could happen
A ludo die lies on the board, not yet thrown.
Outcomes, before any throw
Before the die is thrown, its outcomes are known. They are the six faces, 1 to 6.
Sample space — the list of all outcomes. Event — a group of some outcomes. "An even number" is the event {2, 4, 6}. The brackets { } list the outcomes in the group.
Theoretical probability — the event's outcomes over all outcomes, as a fraction. Its top counts the event's outcomes. Its bottom counts all the outcomes. No throw is needed.
Equally likely is a claim
The counting works only when every outcome is equally likely. That is a claim to check. Do not assume it.
A fair die is equally likely to show each face. "An even number" allows 3 of the 6 faces. Its chance is 3/6 = 1/2. "More than 2" allows 4 of the 6. Its chance is 4/6 = 2/3.
| Set-up | Outcomes | Equally likely? | Example chance |
|---|---|---|---|
| Fair ludo die | 6 faces | yes | even number = 1/2 |
| Marble jar (5 red, 3 blue, 2 green) | 3 colours | no | red = 5/10 = 1/2 |
The jar's three colours are not equally likely. Draw one marble without looking. Then each of the ten marbles is equally likely. Red has five of them: 5/10 = 1/2.
Letters work the same way. Each letter of TAMARIND is on its own card. One card is picked without looking. A is on 2 of the 8 cards. So the chance of A is 2/8 = 1/4. The chance of not A is 1 − 1/4 = 3/4.
Rule: Count the outcomes an event allows. Divide by all the outcomes that can happen. First check they are equally likely.
Count the outcomes that fit. Then pick the chance.
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