Either flip a coin 100 times and report the number of heads, or simply falsify y

Question

Either flip a coin 100 times and report the number of heads, or simply falsify your data by pretending that you flipped the coin 100 times and write down the number of heads that you claim appeared. Do not tell me whether you flipped the coin 100 times, or just made up a number. If you make up a number, make up a number that would make it difficult to suspect that you of falsified data. Thus, the answer to this question is simply the number of heads among 100 tosses of a coin, either real or falsified.

Explanation / Answer

Solution :-

The events are "the number of heads is 0," "the number of heads is 1," "the number of heads is 2" and so on, are very far from being equally likely.

For a fair coin, If you flip it 100 times, then you have 2100= 1.2678 x 1030 different outcomes that are equally likely. This is because any particular sequence of heads and/or tails has probability 1/2n.

As an extreme example, the probability of 0 heads in 100 tosses is 1/220, because there is only 1 pattern of tosses that yields 0 heads.

So, for example, only in 1 out of the 2100 or 2 out of 2100 or so on..

It is not hard to convince yourself that the most occurring outcome is 50% of Heads and 50 % of Tails.

And as we know that larger the sample size the better it reflect the population. And as 100 flips is a large sample it will surely reflect the population, that is a coin when flipped has equal probabilities of landing on Heads or Tails.

So, any number of Heads close to 50 is a good data to show the number of heads appearing either real or falsified.

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