Table of Contents
- 1 How do you simulate an unbiased coin with a biased coin?
- 2 How do you simulate a fair coin with a biased one?
- 3 Can a fair coin be biased?
- 4 How can you generate fair odds using a coin with an unknown bias toward heads or tails?
- 5 What is the probability of getting one head toss of an unbiased coin?
- 6 How do you turn a biased coin into a fair coin?
- 7 Can we generate biased outcomes by combining heads and tails?
How do you simulate an unbiased coin with a biased coin?
The naive way would be throwing the coin 100 times and if the coin came up heads 60 times, the bias would be 0.6….Make a Fair Coin from a Biased Coin.
| Heads | Tails | |
|---|---|---|
| Heads | P ( H H ) = 0.36 P(HH)=0.36 P(HH)=0.36 | P ( T H ) = 0.24 P(TH)=0.24 P(TH)=0.24 |
| Tails | P ( H T ) = 0.24 P(HT)=0.24 P(HT)=0.24 | P ( T T ) = 0.16 P(TT)=0.16 P(TT)=0.16 |
How do you simulate a fair coin with a biased one?
Riddler Classic. Mathematician John von Neumann is credited with figuring out how to take a biased coin (whose probability of coming up heads is p, not necessarily equal to 0.5) and “simulate” a fair coin. Simply flip the coin twice. If it comes up heads both times or tails both times, then flip it twice again.
How do you create an event with a probability of 1/3 using an unbiased coin?
Interview Answers Toss the unbiased coin thrice. Given the outcome is not both tails ( T T) , then the outcome of both heads (H H) has probability 1/3.
Could you tell if a coin is biased?
Note that the coin is biased if it is a physical object as its assymetry means that it won’t be exactly as likely to come down heads as tails.
Can a fair coin be biased?
In probability theory and statistics, a sequence of independent Bernoulli trials with probability 1/2 of success on each trial is metaphorically called a fair coin. One for which the probability is not 1/2 is called a biased or unfair coin.
How can you generate fair odds using a coin with an unknown bias toward heads or tails?
Meaning that we can stop after rolls if one heads has come up since we can create a bipartite matching: HHHT with HHTH, and technically HTHH with THHH although we would already have stopped for those. Similarly, (42) yields the matching HHTT with TTHH (the rest, we would already have stopped before reaching them).
What is the probability of getting one head in one toss of an unbiased coin?
The probability of heads on the first toss is 50\%, just as it is on all subsequent tosses of the coin. The two outcomes of the toss of a coin are heads or tails. For any individual toss of the coin, the outcome will be either heads or tails.
What is biased and unbiased?
In statistics, the bias (or bias function) of an estimator is the difference between this estimator’s expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called unbiased.
What is the probability of getting one head toss of an unbiased coin?
For example, the probability of an outcome of heads on the toss of a fair coin is ½ or 0.5. The probability of an event can also be expressed as a percentage (e.g., an outcome of heads on the toss of a fair coin is 50\% likely) or as odds (e.g., the odds of heads on the toss of a fair coin is 1:1).
How do you turn a biased coin into a fair coin?
There is a simple algorithm to turn a biased coin into a fair one: Flip the coin twice. Identify HT with H and TH with T. Discard cases HH and TT. This algorithm produces a perfectly fair coin, but it is non-deterministic. Deterministic Approximation I also know it is possible to approximate a fair coin with a deterministic algorithm:
How do you find the expected value of a biased coin toss?
The formula for expected value is the sum of each output, multiplied by the probability of that output. So for our biased coin toss the expected value is P (0) * 0 + P (1) * 1 = (1 – x) * 0 + x * 1 = x. Unfortunately this doesn’t get us any closer to solving what x is, or creating our unbiased toss.
How do you find the probability of a coin toss?
First let’s take these bizarre coin side categorisations and make them into something reasonable, like integers, Heads = 1, Tails = 0. Since we know the toss has some biased probability, let’s call this probability x (0 < x < 1). So for any given toss, we have P (1) = x, and P (0) = 1 – x.
Can we generate biased outcomes by combining heads and tails?
I know that by combining heads and tails, we can generate unbiased outcomes using a biased coin. I am trying to understand if we can generate biased outcomes using an unbiased coin.