1What we're really asking
A "match," and how its odds work
You only need two little ideas. Watch each one:
A match = your own hat
A match is when a kid grabs back the exact hat they threw in. We don't care which kid — we just ask: did ANY kid get a match?
Your own odds shrink
With more kids, YOUR own hat is 1 slice out of a bigger pile. So one single kid's chance of grabbing their own hat keeps getting smaller.
2Two ideas pulling opposite ways
Longer odds vs more tries
As the group gets bigger, two things happen at the same time — and they pull the chance of a match in opposite directions:
Each kid's own hat is a tinier slice
More kids → ↓ pulls the chance DOWN. Any one kid almost never grabs their own.
But more kids are each rolling the dice
More kids → ↑ pushes the chance UP. More separate chances for a match.
3Your turn — mix up the hats
Scramble one classroom and see who gets a match
Here's a small class. Tap scramble the hats to throw them in a pile and hand them back at random. A kid glows green if they grabbed their very own hat. Do it a few times — does someone usually match?
4Now go big and run it hundreds of times
100 kids. What are the odds SOMEONE matches? 🎩
One scramble is luck. To find the real chance, we drag the group size and let the computer run the handout hundreds of times, counting how often at least one kid matched. But guess first.
Guess before you run it
100 kids throw their hats in a pile and each grab one at random. What's the chance that AT LEAST one kid gets their very own hat back?