Is it always 50/50 when flipping a coin?

A coin has 2 possible outcomes because it only has two sides (heads or tails). This means that the probability of landing on heads is 1/2. So, the probability of landing on heads is (1/2) x 100, which is 50%.

usmint.gov - Flipping Out for Coins | U.S. Mint for Kids

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Did you enjoy playing the U.S. Mint’s Coin Flip game? Learn more about the history of coin flips, the mathematical origins of coin flips, and history behind the coins featured in the game.

History of Coin Flips

The coin flip dates back to the Roman Empire, where it was originally known as “Heads or Ships”. In more recent years, it has been linked to probability and statistics. In 1903, Orville and Wilbur Wright tossed a coin to decide who would fly first in their historic flight in Kill Devil Hills, North Carolina. The city of Portland, Oregon is rumored to be named as such due to the flip of a coin. Today, a coin toss is used in some sporting events to determine which team will possess the ball.

Probability and Statistics

Coin flips are often used to learn about basic mathematical concepts, including fractions and percentages. They are also used to teach statistical concepts, including probability and relative frequency. Learn more about the mathematical origins of flipping a coin below.

Basic Math

Probability measures the likelihood that an event will occur, such as how likely a coin will land on heads when you flip it. Probability can be represented as a fraction or a percentage. As a fraction, it is represented as:

Desired outcome(s) /# of possible outcomes

When you flip a coin, you choose your desired outcome – the side you want it to land on (either heads or tails). Because you only pick one outcome – let’s say, heads – the desired outcome is 1. A coin has 2 possible outcomes because it only has two sides (heads or tails). This means that the probability of landing on heads is 1/2.

Percentage means ‘out of 100,’ and it can be expressed as:

(Desired outcome(s) / # of possible outcomes) x 100

So, the probability of landing on heads is (1/2) x 100, which is 50%.

Statistics

Based on the calculations we just did, you expect that if you toss a coin 10 times, it will land on heads 50% of the time. If you test this with our Coin Flip game, you’ll see that is not always the case. Why? Try flipping the coin 100 times. Is the number closer to 50%? Most likely, it is. It turns out that the more you do something, like toss a coin, the higher chance you have of reaching the expected probability, which, in this case, is 50%.

Example:

When a coin is flipped 10 times, it landed on heads 6 times out of 10, or 60% of the time. When a coin is flipped 100 times, it landed on heads 57 times out of 100, or 57% of the time. When a coin is flipped 1,000 times, it landed on heads 543 times out of 1,000 or 54.3% of the time. This represents the concept of relative frequency. The more you flip a coin, the closer you will be towards landing on heads 50% – or half – of the time.

Historical Coins

Learn more about the coins featured in the Coin Flip game in the gallery below.

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