# What is a Fair and Unfair coin?

• Last Updated : 30 Dec, 2021

Probability refers to the chances of occurrence of a wanted outcome out of all the given possible outcomes of an event. The wanted outcome of the probability even is called Favorable Outcome and all other outcomes other than the wanted outcome fall in the category of Unfavorable Outcome. In simple terms, probability gives the extent of how likely an outcome can occur out of all the possible outcomes available.

### Probability of an Event

Probability events predict the likeliness of outcomes based on how the probability event is carried out. There are mainly two types of the probability of an event, they are fair probability events and unfair probability events. Probability of an event is given as,

Probability of an Event = Chances of occurrence of a Wanted Outcome/ Total number of possible outcomes of the Event

• Fair Probability Events

Probability Events are known as Fair Probability Events when they demonstrate fair practices and each outcome has an equal chance of being the final outcome of the probability event. Fair Probability Events follow probability principles and there is no partialism shown towards an outcome be it a wanted or unwanted outcome. All outcomes are considered equal and have an equal chance of occurrence.

• Unfair Probability Events:

Probability Events are known as Unfair Probability Events when they demonstrate unfair practices and each outcome has an unequal chance of being the final outcome of the probability event. Fair Probability Events doesn’t follow probability principles and there is partialism shown towards an outcome be it a wanted or unwanted outcome. All outcomes are not considered equal and don’t have an equal chance of occurrence.

### What is a Fair and Unfair Coin?

• Fair Coin

A coin is said to be a Fair Coin when it behaves like a generic coin. Fair Coin has the same outputs as the generic coin i.e; a Fair Coin has two outputs – One Head & One Tail.

Probability of Heads while tossing of a coin,

= Number of Heads on Sides of Coin / Total Outputs for Coin

= 1/2

Probability of Tails while tossing of a coin,

= Number of Tails on Sides of Coin / Total Outputs for Coin

= 1/2

• Unfair Coin

A coin is said to be an Unfair Coin when it doesn’t behave like a generic coin. Unfair Coin does not have the same outputs as the generic coin i.e; an Unfair Coin has either Two Heads or Two Tails.

Thus unfair coin can have two cases of Probability,

• Case 1: When both the outputs are Heads

Probability of Heads while tossing of a coin,

= Number of Heads on Sides of Coin / Total Outputs for Coin

= 2/2

= 1

• Case 2: When both the outputs are Tails

Probability of Tails while tossing of a coin,

= Number of Tails on Sides of Coin / Total Outputs for Coin

= 2/2

= 1

### Similar Problems

Question 1: Is throwing a dice fair?

A generic dice has six numbers ranging from 1 to 6 on all its faces. To check if a dice is fair, compare the available outputs to the outputs of a generic dice and then conclude if it’s a fair dice or not.

Question 2: Do probabilities vary when we consider fair and unfair scenarios of probability?

Yes, probability varies when the two scenarios of fair and unfair probabilities are considered. Since the outputs in both cases are different, therefore, the probabilities linked to them are also different.

Question 3: A coin is tossed. Would it be considered a fair or unfair coin?