Marbles in a bag

The oldest probability lesson there is

Three red and one blue is where every probability lesson starts, because everybody can see the answer before they can write it down. Three out of four. Seventy-five percent. The bag on this page shows both forms at once, next to the marbles themselves, so the fraction and the percentage and the handful of counters are visibly the same fact.

You can hide the table when the point is for the class to work it out, and put it back the moment somebody wants to check. Nothing is timed and nothing is scored: it is a bag, and it does what a bag does.

Experimental against theoretical

The interesting lesson is the gap. Set three red and one blue with replacement on, draw twenty times, and tally what actually comes out. It will not be fifteen and five, and the argument about why not is the whole of the topic. Draw a hundred times and it gets closer, which is the next lesson after that.

Drawing several at once makes that quick: ten marbles a press, with the results stacked up beside the bag. For a bag where nothing comes back, the bag of tokens does the same job with your own words instead of colours.

With and without replacement

These are two different bags and it is worth saying so out loud. Put the marble back and every draw is independent: the bag has no memory, the odds never move, and a run of four reds means nothing at all about the fifth.

Leave it out and every draw changes the next one. The last blue leaves the bag and blue drops to zero in front of everybody, which is much harder to argue with than a sentence about conditional probability. For picking names rather than colours, the wheel and the bag of tokens are the tools next door.

Nothing to install, nothing to sign up for

The tool runs entirely in your browser. There is no account, nothing you make is uploaded, and nothing you type is sent anywhere or put into a link.

The page itself is not silent, though: it carries advertising code and a visit counter that sets no cookie, and the cookie page says exactly what each of those does.

This page remembers your settings in your browser under pph.marbles.bag, pph.marbles.replace, pph.marbles.count, pph.marbles.odds and pph.marbles.muted, and nowhere else. Clearing your site data for papercarnival.com removes it.