flip 5 coinsFlip 5 coins

Flip five coins at once

Five coins in a row. Tap them, press Flip or hit the Space bar, and each one comes down heads or tails independently. The result shows how many of each, and the running tally at the bottom adds up every coin you have flipped until you press Reset.

A majority vote that cannot tie

With an odd number of coins there is always a majority. Five coins give a decision that feels weightier than a single flip, and the odds are still exactly even: heads wins the majority half the time. A clear sweep, five out of five, is rare: it happens 1 time in 16 for either side, 6.25% in total. Lopsided results such as 4 to 1 are more common than many people expect, together about 31% of flips.

A binomial experiment in your pocket

Five coins are a neat way to meet the binomial distribution. Each coin is a yes or no trial with a one in two chance, and the number of heads goes from 0 to 5. There are 32 equally likely sequences, and the number of sequences with a given count of heads follows the row 1, 5, 10, 10, 5, 1 of Pascal’s triangle. The exact table below shows the same numbers as chances.

• Flip 50 times and tally how often you get 0, 1, 2, 3, 4 and 5 heads.
• Compare your tally with the table: 2 and 3 heads should dominate, 0 and 5 should be rare.
• Combine results from the whole class to watch the counts get closer to the exact chances.

Prefer to see the sequence rather than the count? Read the coins left to right, as five flips of a single coin in a row: the odds are the same.