Four experiments in chance and uncertainty. Slide, roll, and click your way through the chapter's core ideas — no coin or die required, they're all built in.
From impossible to certain
0 to 1
Slide to change how many of the six cards are purple. Watch the probability of drawing a purple card move smoothly along the scale — from impossible, through less likely, even chance, and more likely, up to certain.
slide to change the deck
Readings
Purple cards—
Green cards—
P(purple)—
In words—
0 purple cards is impossible; 6 purple cards is certain. Everything in between is some shade of "maybe".
Watching the Law of Large Numbers
§7.2.1
Roll a fair six-sided die again and again. Each bar shows how often a face has actually come up so far (experimental probability); the dashed line marks the theoretical probability, 1/6. Watch the bars settle toward the line as the rolls pile up.
Readings
Total rolls0
Theoretical P(any face)0.1667
Furthest bar from theory—
With 0 rolls there's nothing to compare yet — start rolling!
Building a tree diagram
§7.3 & §7.4
Pick what happens at each step, then click leaves on the right to build your own event. The probability of your event is just the sum of the probabilities of the outcomes you selected.
click a leaf to add/remove it from your event
Readings
Total outcomes n(S)—
Outcomes in your event0
P(your event)0
Try selecting every leaf where step 1 is "Heads" — the event probability should land on exactly 0.5.
Does the coin remember?
Gambler's Fallacy
Flip a fair coin as many times as you like. However long a streak of heads (or tails) builds up, the next flip is still a plain 50/50 — the coin has no memory of what came before.
Readings
Total flips0
Current streak—
Longest streak seen0
P(next flip is heads)0.5
However long the streak on the left gets, that last number never moves off 0.5. That's the whole fallacy, in one statistic.