Question

A coin is tossed 10 times and the results are 2 tails and 8 heads. How will you analyse whether the coin is fair or not? What is the p-value for the same?

Answer 1

The distribution of the number of (say) heads is Binomial. The p-value is the probability of obtaining a number of heads that is as extreme or more extreme. You can test (for example) if the probability of the coin yielding heads is different from 1/2. Then the p-value is the probability of getting 1,2,9, or 10 heads (you can also add 3 and 8 if you opt for a non-strict inequality). We reject the hypothesis that the coin is fair if the p-value is too small (i.e. if we have witnessed an event that is highly unlikely given our assumption).