Are coins fair?
If the coin is tossed and caught, it has about a 51% chance of landing on the same face from which it was launched. Spun coins can exhibit “huge bias” (some spun coins will fall tails-up 80% of the time). In other words, no spinning if you want to play fair – only tossing.
What is meant by a fair coin?
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 do you simulate a fair coin with an unfair coin?
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.
Can a coin flip be biased?
The 2007 Diaconis – Holmes – Montgomery paper Dynamical bias in the coin toss suggests that in coin-tossing there is a particular “dynamical bias” that causes a coin to be slightly more likely to land the same way up as it started.
Can a coin toss be inconsistent with fairness?
Sometimes it can show you that your coin-tossing-process on a given coin is inconsistent with fairness, but failure to identify any inconsistency with fairness doesn’t imply fairness (failure to reject is because your sample size is small, not because the coin is actually fair).
Can a coin be fair in a two tailed test?
That’s clearly an unfair coin, but you’ll reject barely more often than your type I error rate, and a large fraction of those rejections in a two tailed test would be “in the wrong tail”!] No coin-tossing process on a given coin will be perfectly fair.
How to calculate the probability of 10 tosses of a coin?
So, to compute the p-value in this situation, you need only compute the probability of 8 or more heads in 10 tosses assuming the coin is fair. But, the number of heads in 10 tosses of a coin assuming that the coin is fair has a binomial distribution with n=10 and p=0.5.
How is an interview problem like a coin?
An interview problem is like the following: Given a coin you don’t know it’s fair or unfair. Throw it 6 times and get 1 tail and 5 head. Determine whether it’s fair or not.