Does Coin flip really a 50–50 probability?

Coin Toss Probability is the probability of events involving coins and as we know, probability is the branch of mathematics that deals with the possibility of success or failure for any event. Mathematically, the probability is the ratio of the number of favorable outcomes to the total number of outcomes (sample space) for an event.

In simple words, coin toss probability is one part of the probability in which we find the probability of tossing a coin or multiple coins. Theoretically, for a fair coin, the probability of getting a head after a coin toss is 50% or 1/2 (As a coin has two sides Head and Tail) but in real life, it is not. This article answers the question i.e., “Does Coin flip really has a 50–50 probability?”, and also gives us brief information about coin toss probability. So, let’s verify does the coin toss probability has a 50-50 probability or not.

Coin Toss Probability Formula

Let E be the event of tossing a coin and getting the desired outcomes and S be the sample space, then probability P(E) is given by:

P(E) = n(E) / n(S)

Probability of getting a head or tail when a coin is tossed is:

P(H) = P(T) = 1 /2

Read more about Coin Toss Probability.

Does Coin Flip have a 50-50 Probability?

Theorecitcal probability of any fair and unbiased should indeed have a 50-50 probability of landing heads or tails which mean each outcome in two outcomes should be head or tail. But in real life as there are various factors in real life which can affect the results of the coin toss, thus the coin flip really does not have a 50-50 probability. Some of these factors are:

• The way in which the coin is flipped or tossed up in the air can affect the resultant outcome of the flip.
• The surface where the coin is flipped can affect the outcome as the coin can roll or sink slightly from the final position.
• The imperfections in the coin can be one of the factors.
• The height from which the coin is being tossed or flipped can affect the resultant outcome.

These Facorts have very small bias in the outcome of Coin Flip, but these surely effect the result such the resulting probability becomes close to 51/49 baised towards whichever side is up while tossing the coin. So, the coin flip really does not have a 50-50 probability but 51-49, biased towards the side which is facing upward during the coin toss.

What is Biased Coin?

The coin in which the outcomes are not equally likely is called as the biased coin. The coin whose two sides have different probabilities. The probability of getting one side on the biased coin is not equal to 1/2. The biased coin is also known as the unfair coin. The side whose probability is greater than 1/2, the outcome is biased towards that side.

Biased Coin Vs Unbiased Coin

The key difference between biased coin and unbiased coin are as follows:

Biased Coin	Unbiased Coin
The coin whose outcomes are not equally likely is called biased coin.	The coin whose outcomes are equally likely is called unbiased coin.
It is also called as unfair coin.	It is also called as fair coin.
In biased coin, the two sides have two different probabilities.	In unbiased coin, the two sides have same probabilities.
The probability of getting one side is not equal to 1/2.	The probability of getting one side is equal to 1/2.

Read More,

• Permutations and Combinations
• Binomial Theorem
• Probability Distribution

FAQs on 50-50 Probability of Coin Flip

1. What is Coin Toss Probability?

The probability for any event while tossing coin is called as coin toss probability.

2. Write the formula for finding probability.

The formula for finding probability is given by:

Probability of any event = Number of favorable outcomes / Total number of outcomes

3. What is the sample space when two coin is tossed?

The sample space when two coin is tossed is given by: S = {(H, H), (H, T), (T, H), (T, T)}.

4. Define Biased Coin.

The coin in which the probability of the two sides is not equal is called biased coin.

5. What is Unbiased Coin?

The coin in which the probability of the two sides is equal is called unbiased coin.

6. What is Fair Coin?

The coin whose outcomes are equally likely is called fair coin.

7. What is the Key difference between Biased and Unbiased Coin?

The key difference between the biased and unbiased coin is that in biased coin the probability of both the sides are unequal and not equal to 1/2 whereas in unbiased coin the probability of both the sides are equal and equal to 1/2.

8. What is the Probability when an Unbiased Coin is Tossed?

The probability when an unbiased coin is tossed is 1/2.