Dice can be loaded—that is, one can easily alter a die so that the probabilities of landing on the six sides are dramatically unequal.
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.
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.
Simply flip the coin twice. If it comes up heads both times or tails both times, then flip it twice again. Eventually, you'll get two different flips — either a heads and then a tails, or a tails and then a heads, with each of these two cases equally likely.
To estimate the bias, we toss the coin n times and count how many Heads we observe. Then our estimate of the bias is given by ^p=Sn/n p ^ = S n / n , where Sn is the number of Heads in the n tosses.
When we talk about a coin toss, we think of it as unbiased: with probability one-half it comes up heads, and with probability one-half it comes up tails. An ideal unbiased coin might not correctly model a real coin, which could be biased slightly one way or another. After all, real life is rarely fair.
The coin is tossed repeatedly till a "head" is obtained. If the tosses are independent, then the probability of getting "head" for the first time in the fifth toss is . 0.072.
Suppose you need to simulate an unfair coin that has a probability of 1/4 = 0.25 for getting Heads. You can easily do that by flipping the fair coin twice. Report success ( 1 ) if you get 2 Heads, and report failure ( 0 ) otherwise.
However, even on a flat surface it is possible for a coin to land on its edge. A computational model suggests that the chance of a coin landing on its edge and staying there is about 1 in 6000 for an American nickel.
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.
In the United States, U.S. Code Title 18, Chapter 17, Section 331 prohibits "the mutilation, diminution and falsification of United States coinage." The foregoing statute, however, does not prohibit the mutilation of coins, if the mutilated coins are not used fraudulently, i.e., with the intention of creating ...
After two and six months participants were contacted again and asked about their decision and associated satisfaction. His study revealed that individuals who were told by the coin toss to make a change (compared to maintain the status quo) were much more likely to make the change and were happier six months later.
Here is that surprising approach to decision making: Flip a coin. The coin flip is used to help us test our gut feel or our intuition. All the while you have been pondering a decision consciously, looking at the data, doing pros and cons lists, and perhaps talking to others, your subconscious has been at work too.
Bias is a component of fairness—if a test is statistically biased, it is not possible for the testing process to be fair.
The statement that 'Bias is a kind of chance error' is false. Bias affects all measurements the same way, pushing them in the same direction. Chance errors change from measurement to measurement, sometimes up and sometimes down.
Risks of bias are the likelihood that features of the study design or conduct of the study will give misleading results. This can result in wasted resources, lost opportunities for effective interventions or harm to consumers.
What he and his fellow researchers discovered is that most games of chance involving coins aren't as even as you'd think. For example, even the 50/50 coin toss really isn't 50/50 — it's closer to 51/49, biased toward whatever side was up when the coin was thrown into the air.
A coin has 2 possible outcomes because it only has two sides (heads or tails). This means that the probability of landing on heads is 1/2. So, the probability of landing on heads is (1/2) x 100, which is 50%.
Coin tosses can be biased only if the coin is allowed to bounce or be spun rather than sim- ply ipped in the air.
An unfair coin is one which has unequal probabilities of landing heads-up and tails-up when flipped. A Bernoulli trial is a random experiment with 2 possible outcomes, generally designated as success and failure, or as the corresponding numeric values 1 and 0.
Discussion: This is originally von Neumann's clever idea. If we have a biased coin (i.e. a coin that comes up heads with probability different from 1/2), we can simulate a fair coin by tossing pairs of coins until the two results are different.
If a coin is flipped with its heads side facing up, it will land the same way 51 out of 100 times, a Stanford researcher has claimed.
The theory the researchers give to explain this phenomenon is that flipping a coin makes the consequences of a decision more real, and therefore makes one's feelings about that decision stronger. Once the coin flip has committed you to one option or another, you realize which outcome you wanted all along.