🧱 See It
Picture a bag with 3 red marbles and 2 blue marbles — 5 marbles total. You reach in without looking and pull one out.
3 red marbles, 2 blue marbles — 5 marbles in the bag altogether.
✏️ Draw It
To find the chance of pulling red, first lay out every single marble in a row — the whole bag, nothing left out. Then mark the ones that count as "red."
3 marbles circled as "favorable" (red) out of 5 marbles total.
3 out of 5 marbles are red.
🔢 Write It
Probability compares favorable outcomes to all possible outcomes:
P(event) = favorable outcomes ÷ total outcomes
For pulling a red marble:
P(red) = 3 ÷ 5 = 3/5
💡 Worked Examples
Example 1 — Theoretical: a spinner
A spinner is split into 4 equal sections. Only 1 section is labeled "WIN."
- Total outcomes: 4 equal sections.
- Favorable outcomes: 1 section labeled "WIN."
- Answer:
P(win) = 1 ÷ 4 = 1/4
This is theoretical probability — figured out just by counting sections, before ever spinning it.
Example 2 — Experimental: flipping a coin
A coin was flipped 20 times. Here's what actually happened:
| Outcome | Times it happened |
|---|---|
| Heads | 12 |
| Tails | 8 |
- Total trials: 20 flips.
- Favorable outcomes: 12 heads.
- Answer:
experimental P(heads) = 12 ÷ 20 = 3/5
But theoretically, a fair coin has 2 equally likely sides, so P(heads) = 1/2. The real trial gave 3/5 instead of 1/2 — close, but not exact. That's normal for a small number of trials!