Lay every combo in a grid.

Four words, then you're set.

These come up on every probability page, so let's pin them down once, in plain language:

• An outcome is one single way something can turn out — for one coin, that's "heads" or "tails."
• The sample space is the whole list of possible outcomes — every square in the grid, together.
• A combined event is two (or more) events happening together — like tossing a coin and rolling a die in the same go.
• The favourable outcomes are the ones you're hoping for — the squares that count as a "win" for the question you're asking.

Keep those four in your pocket. Probability of the thing you want is always just favourable outcomes ÷ total outcomes — the shaded squares over all the squares.

Build the grid, pick a target, read the odds.

Choose which two events happen together. The table fills with every combination. Then pick a target and watch the shaded squares — and the probability — appear. Click any single square to see its own tiny chance.

Two coins make four squares.

Set the table above to Two coins and count with me. Each coin can land two ways, heads (H) or tails (T). Put the first coin down the side and the second across the top, and you get a tiny 2×2 grid — four squares in all:

Notice how each square is equally likely: with fair coins, no combination is special. That's why we're allowed to just count. If the squares weren't all equally likely, counting alone wouldn't be enough — but for fair coins and fair dice, it always is.

Two dice make thirty-six squares.

Switch the table to Two dice. Each die shows 1 to 6, so the grid grows to 6 rows by 6 columns — 6 × 6 = 36 squares, one for every pair like (3,5) or (6,1). That's the whole sample space for a pair of dice.

Here's the classic question: what's the chance the two dice add up to 7? Highlight the "sum = 7" target and count the shaded squares. You'll find exactly six of them, running in a neat diagonal:

Try a few more targets and watch the diagonals shift. "Doubles" (both dice the same) is another 6 squares — 636 = 16. "Snake eyes" (sum = 2) is a lonely single square, 136 — the rarest thing on the board. And "at least one 6" lights up a whole row and column, 11 squares, 1136. The grid never lies: every question is just how many squares fit.

Why the possibilities multiply.

Here's the shortcut that saves you from ever drawing a giant grid by hand. To get the total number of squares, you multiply the number of ways each event can turn out. Two coins: 2 × 2 = 4. Two dice: 6 × 6 = 36. A coin and a die: 2 × 6 = 12.

Why multiply? Because for every one of the first event's outcomes, the second event can still do all of its outcomes. Each of the 2 coin results opens up all 6 die results, so you stack 6 on top of 6 — that's the grid growing sideways and downward at the same time. Add a third event and it multiplies again. Build a lineup below and watch the total climb:

The two events don't have to match.

Nothing says both events have to be the same. Toss a coin and roll a die together and you've combined a 2-outcome event with a 6-outcome event. Set the table to Coin + die and you'll see a 2×6 grid — 2 × 6 = 12 squares, from (H,1) all the way to (T,6).

This is the real power of the grid: it doesn't care what the two events are. Coin and die, die and spinner, card and coin — lay them on two axes, fill the squares, count what you want. The method never changes.

Your turn — no grid to peek at.

Four quick questions. Think in squares: favourable over total. Tap your answer to see if it lands.