flip 2 coinsFlip 2 coins

Flip two coins at once

Two coins sit side by side, ready to toss. Tap them, press Flip or hit the Space bar: both spin, land, and the result reads as a count of heads and tails. The bar at the bottom keeps a running tally until you press Reset.

Three results, but not equally likely

With two coins you can see two heads, two tails, or one of each. It is tempting to think each has a one in three chance. It does not: the coins are distinct, so “one of each” can happen two ways, heads then tails or tails then heads. Two heads comes up a quarter of the time, two tails a quarter, and one of each half the time.

Even great mathematicians have slipped here. In 1754, Jean le Rond d’Alembert argued in the article “Croix ou pile” of the French Encyclopédie that the chance of getting at least one head in two tosses was two in three. The correct answer is three in four, because the outcome he merged into one case is really two.

Two-up

Australia has a game built on exactly this. In two-up, a “spinner” tosses two coins from a small wooden paddle called a kip. Two heads and the heads backers win; two tails and the tails backers win; one of each, called “odds”, and the coins are tossed again. It is traditionally played on Anzac Day. You can run a friendly round here: flip, and flip again on odds.

Other uses

• A probability lesson: flip 40 or 100 times, note the counts and compare with a quarter, a half and a quarter.
• A double decision: one coin for each question, such as “indoors or out?” and “pizza or pasta?”.