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.
FAQs
The experiment involved 48 people flipping coins minted in 46 countries (to prevent design bias) for a total of 350,757 coin flips. Each time, the participants noted whether the coin landed with the same side up as when it was launched. The researchers found that Diaconis was right—there was a slight bias.
What's the chance that you get 5 heads when you flip a coin 10 times? ›
Answer and Explanation:
Consider we toss a coin, the probability of getting head is equal to 0.5 ( p = 0.5 ) . Because, if we toss a coin, then there are two possible outcomes either we get a head or a tail. Thus, the probability of getting 4 or 5 heads out of the 10-coin tosses is 0.451.
What do you say when you flip a coin? ›
We flip or toss a coin and call heads or tails. “Heads you win.” or “Tails I win.” Whosever call matches the side of the coin showing is the winner.
Is there a trick to coin flip? ›
Rest the coin on the back of your thumb with your index finger wrapped around it. As you toss, don't flick your thumb but instead use your index finger to spin the coin like a frisbee. Practice this move until you've got it down pat.
How do you teach coins to value to kids? ›
Teaching the values of coins requires showing the worth of each coin in cents. This instruction is done by placing cutouts representing the values of each coin on top of the cent model. The number of cent units covered by a coin model represents the value of the coin.
Is flipping a coin exactly 50/50? ›
It does depend on the technique of the flipper. Some people had almost no bias while others had much more than 50.8 percent, Bartos said. For people committed to choosing either heads or tails before every toss, there was no bias for either side, the researchers found.
What is the Coin Flip theory? ›
Flipism is a normative decision theory in a sense that it prescribes how decisions should be made. In the comic, flipism shows remarkable ability to make right conclusions without any information—but only once in a while. In reality, flipping a coin would only lead to random decisions.
What lands more, heads or tails? ›
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%.
What happens if you toss a fair coin 5 times? ›
Since toss of each coin can result in 2 ways. When coin is tossed five times, the total number of outcomes = 2×2×2×2×2=32 Hence, required number of ways is 32.
What are the odds of flipping a coin heads 10 times in a row? ›
While incredibly unlikely, there is still a 0.0977% chance of getting 10 heads in a row.
Similarly, there is only one way to have all 12 flips land on heads, because if any of them were not a head, then it would not be all heads, so the probability of getting all heads is the same as the probability of getting all tails. That is, it is 1 divided by 4096, or , which has an approximate value of 0.000244.
What to pick when flipping a coin? ›
Next time you flip a coin you might want to pick the side that's already facing up Researchers find flipped coins have what's called same side bias. They flipped coins in 46 currencies 350,000 times, and registered that 51% of the time the coins landed on the side they started on.
How to predict coin flip? ›
How do you predict a coin flip? Tossing a coin is a random experiment, as you do know the set of outcomes, but you do not know the exact outcome for a particular execution of the random experiment. Therefore, we cannot predict a coin flip if the coin is fair.
What are the rules of a coin flip? ›
Either beforehand or when the coin is in the air, an interested party declares "heads" or "tails", indicating which side of the coin that party is choosing. The other party is assigned the opposite side. Depending on custom, the coin may be caught; caught and inverted; or allowed to land on the ground.
Which is more likely, head or tail? ›
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.
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.