When experimental results match one’s expectations perfectly, there may be cause for rejoicing. often there is not a perfect match, however, and doubts arise about the accuracy and adequacy of the data. would you demand a perfect result of 5 heads and 5 tails to consider the trial to be a fair one? if not, how far off would you allow the result to be before you became suspicious of a trick? decide that this is acceptable?

No, I would not demand a perfect result of 5 heads and 5 tails to consider the trial a fair one.

Explanation:

Flipping a coin is an example of an experiment or trial that has what is known is statistics a binomial probability distribution. An experiment has a binomial probability distribution when it has two possible outcomes: in this case, either getting a head or a tail.

While in theory the probability of getting a head or a tail is both 50%, this does not mean than if you run the experiment, you will always get a head for each tail or viceversa, it can happen that you get more tails or more heads after flipping the coin.

Let's suppose that you flip the coin ten times as stated in the question. In theory, the results could be: 5 heads and 5 tails, but the results could also be 7 heads and 3 tails, or even 9 heads and 1 tail, and while these two last outcomes are less probable, their probability is still higher than 0%.

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