Contents

- 1 How do you make a fair decision with unfair coins?
- 2 How a biased coin can be made into unbiased?
- 3 How do you simulate an unbiased coin with a biased coin?
- 4 Can a coin be unfair?
- 5 How can you tell if a given coin is biased?
- 6 Is a coin biased?
- 7 How do you solve a biased coin problem?
- 8 What is biased and unbiased coin?
- 9 What is the probability of flipping an unfair coin?
- 10 What is fair and unfair coin?
- 11 What is the probability of getting four tails and two heads when an unfair coin is tossed 6 times?
- 12 What is the entropy of flipping a biased coin?
- 13 How do you make a fair coin out of a biased one?
- 14 Is tossing a biased coin binomial?

## How do you make a fair decision with unfair coins?

How can you use a biased coin to make an unbiased decision? That is to say the coin does not give heads or tales with equal probability. Von Neumann wrote it like this:

- Toss the coin twice.
- If the results match, start over, forgetting both results.
- If the results differ, use the first result, forgetting the second.

## How a biased coin can be made into unbiased?

If the coin lands with two different results, Tails Heads, or Heads Tails, we invert the second, and take the doubled up result as the answer to our coin flip. Since the order of the flips is independent, it doesn’t matter what the bias is, we still have equal chance of these outcomes, so it’s a 50/50 unbiased coin.

## How do you simulate an unbiased coin with a biased coin?

Von Neumann described this procedure like this:

- Toss the coin twice.
- If the outcome of both coins is the same (HH or TT), start over and disregard the current toss.
- If the outcome of both coins is different (HT or TH), take the first coin as the result and forget the second.

## Can a coin be unfair?

Coin tosses can be biased only if the coin is allowed to bounce or be spun rather than simply flipped in the air. The biased coin is the unicorn of probability theory—everybody has heard of it, but it has never been spotted in the flesh.

## How can you tell if a given coin is biased?

There are two ways to determine if a coin is biased or fair. The most common way is to flip the coin a bunch of times and see what fraction are heads. If you only flip it 10 times and get 3 heads, there is little to conclude. But if you flip it 1000 times and get 300 heads, it almost certainly is biased.

## Is a coin biased?

Coin tosses can be biased only if the coin is allowed to bounce or be spun rather than sim- ply ipped in the air.

## How do you solve a biased coin problem?

Let us flip the coin twice. If it comes up heads first and tails second, then we call it a 0. If it comes up tails first and heads second, then we call it a 1. If the two flips are the same, we flip twice again, and repeat the process until we have a unbiased toss.

## What is biased and unbiased coin?

Unbiased coin has equal probability of Heads or Tails. If you throw the coin a million times, you will get 500,000 heads and 500,000 tails. A biased coin has a higher probability of heads or tails. This is generally done by making the coin imbalanced.

## What is the probability of flipping an unfair coin?

The probability is 0.6 that an “unfair” coin will turn up tails on any given toss.

## What is fair and unfair coin?

A fair coin has an exactly equal chance of landing heads or tails face up when flipped. An unfair coin is one that has been tampered with in some way to give a greater chance to either heads or tails being the outcome of a flip.

## What is the probability of getting four tails and two heads when an unfair coin is tossed 6 times?

When 6 coins are tossed at a time; total number of possible outcomes = (2*2*2*2*2*2) = 2^6 = 64. Therefore, there are (15 + 6 + 1) = 22 possible outcomes leading us to get 4 or more heads. Therefore, probability of getting 4 or more heads = (22 / 64) = (11 / 32).

## What is the entropy of flipping a biased coin?

As an example, consider a biased coin with probability p of landing on heads and probability 1 − p of landing on tails. The maximum surprise is for p = 1/2, when there is no reason to expect one outcome over another, and in this case a coin flip has an entropy of one bit.

## How do you make a fair coin out of a biased one?

You are given a function foo() that represents a biased coin. When foo() is called, it returns 0 with 60% probability, and 1 with 40% probability. Write a new function that returns 0 and 1 with a 50% probability each.

## Is tossing a biased coin binomial?

Binomial Distribution. When you flip a coin, there are two possible outcomes: heads and tails. In the case of coins, heads and tails each have the same probability of 1/2. More generally, there are situations in which the coin is biased, so that heads and tails have different probabilities.