🧱 See It
Before, probability meant one thing happening: one coin flip, one spinner. Now picture two things happening at the same time: flip a coin AND roll a die.
These are independent events — the coin has no idea what the die is doing, and the die has no idea what the coin landed on. Each one still behaves exactly the way it would on its own.
Coin: 2 possible outcomes. Die: 6 possible outcomes. Neither one changes the other.
✏️ Draw It
With one event, you laid out every outcome in a row. With two events at once, lay out every pairing in a table — every coin side crossed with every die number:
| 1 | 2 | 3 | 4 | 5 | 6 | |
|---|---|---|---|---|---|---|
| Heads | H1 | H2 | H3 | H4 | H5 | H6 |
| Tails | T1 | T2 | T3 | T4 | T5 | T6 |
12 boxes, 12 possible pairings — every one written out, none left to guess at.
🔢 Write It
To find the total number of pairings without drawing the whole table every time, multiply the number of outcomes for each event:
total outcomes = (outcomes of event 1) × (outcomes of event 2)
For a coin and a die:
2 × 6 = 12 total outcomes
Then probability still works the same way as always:
P(event) = favorable pairings ÷ total pairings
💡 Worked Examples
Example 1 — Theoretical: P(Heads AND rolling a 4)
- Total outcomes:
2 × 6 = 12 - Favorable outcomes: only H4 matches — that's 1 pairing.
- Answer:
P(H and 4) = 1 ÷ 12 = 1/12
Example 2 — Experimental vs. theoretical: "Heads and an even number"
A coin and a die were flipped/rolled together 24 times. "Heads and an even number" happened 5 of those times.
- Total trials: 24.
- Times it happened: 5.
- Experimental answer:
experimental P = 5 ÷ 24
Now compare that to the theoretical probability, using the table: the favorable pairings are H2, H4, H6 — 3 pairings out of 12 total.
theoretical P = 3 ÷ 12 = 1/4
5/24 is close to 1/4 (which is 6/24) but not exactly equal — and that's expected. Experimental results don't have to match the theoretical probability exactly, especially with a small number of trials.