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How to make a Fair Coin from a Biased Coin?

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  • Last Updated : 19 Jan, 2022

Probability is the measure of how often is the chance of a likeable outcome appearing out of all the possible outcomes. Probability gives the chance of a desired or wanted outcome to be the final outcome of the Probability Event. All other outcomes apart from the wanted outcome fall in the category of an unwanted outcome. Sum of probabilities of wanted and unwanted outcomes together total to one. Probability in the Mathematics world gives a ratio of the Wanted Outcome upon the Total Outcomes of the Probability Event.

Probability of an Event = Total Chances of Wanted Outcome to Appear/ Total Outcomes

There are two broad categories of Probability, based on the manner in which probability events are carried out:

  • Fair Probability: Probability scenario where the generic probability principles and rules are applied and each outcome is given appropriate consideration for being the final outcome of the probability scenario, fall in this category of Fair Probability Event.
  • Unfair Probability: Probability scenario where the generic probability principles and rules are not applied and each outcome is not given appropriate consideration for being the final outcome of the probability scenario, fall this category of Unfair Probability Event.

Now we discuss Fair and Unfair coins:

Fair Coin

A fair coin has one head and one tail. Both of these outcomes have an equal chance of being the final outcome of the event. The probability of heads appearing for a fair coin is 1/2. Similarly, the probability of tails for a fair coin is 1/2.

One Pair of outcomes for a fair coin: One Head and One Tail

Unfair Coin

A fair coin has one head and one tail. Both of these outcomes have an equal chance of being the final outcome of the event. The probability of heads appearing for an unfair coin is 2/2 or 1. Similarly, the probability of tails for an unfair coin is 2/2 or 1.

Two Pairs of possible outcomes of an unfair coin:

  • Two Heads
  • Two Tails

How to make a Fair Coin from a Biased Coin?

Solution:

Yes, it is possible to transform an unfair coin into a Fair. To make an unfair coin fair, follow the below steps:-

Step 1: Calculate the total outputs of the given coin.

Step 2: Compare the outputs with a generic coin.

Step 3: Replace the output which exceeds the output that’s not present.

Step 4: Recheck and match both the outputs. The outputs should replicate the outputs of a Generic Coin.

Example:

We have an unfair coin with two tails. Now we make an unfair coin to fair using the following steps:

Step 1: Calculate the total outputs of the given coin. Here, we find that both the outputs are tails.

Step 2: Compare the outputs with a Generic Coin (One Head and One Tail).

Step 3: Replace the output which exceeds with the output that’s not present. Here, tail is the output which exceeds and heads is the output which is not present. So, we will replace one tails with one heads.

Step 4: Recheck and match both the outputs. The outputs should replicate the outputs of a generic coin. The outputs of the coin should be one heads and one tails.

Similar Questions

Question 1. List the outputs of a Generic Coin.

Solution:

A Generic Coin has One Head and One Tail.

Question 2. Give the Probabilities of each Outcome of a Fair Coin.

Solution:

Probability of Heads = 1/2

Probability of Tails = 1/2

Question 3. How to check if a Coin is Fair or Unfair.

Solution:

Calculate the outputs of the given coin. Compare the outputs with a generic coin output (One Heads and One Tails). If the outputs match with that of a generic coin, then the coin can be called a fair coin.

Question 4. What are the traits of an Unfair Coin?

Solution:

An Unfair Coin has either Two Heads or Two Tails.

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