Other Applications
The above mathematical analysis for determining if a coin is fair can also be applied to other uses. For example:
- Determining the proportion of defective items for a product subjected to a particular (but well defined) condition. Sometimes a product can be very difficult or expensive to produce. Furthermore, if testing such products will result in their destruction, a minimum number of items should be tested. Using a similar analysis, the probability density function of the product defect rate can be found.
- Two party polling. If a small random sample poll is taken where there are only two mutually exclusive choices, then this is similar to tossing a single coin multiple times using a possibly biased coin. A similar analysis can therefore be applied to determine the confidence to be ascribed to the actual ratio of votes cast. (Note that if people are allowed to abstain then the analysis must take account of that, and the coin-flip analogy doesn't quite hold.)
- Finding the proportion of females in an animal group. Determining the gender ratio in a large group of an animal species. Provided that a small random sample (i.e. small in comparison with the total population) is taken when performing the random sampling of the population, the analysis is similar to determining the probability of obtaining heads in a coin toss.
Read more about this topic: Checking Whether A Coin Is Fair