We can do this by making use of the binomial equation and setting the number of successes, r, to 0, and the number of trials, n, to 20. Consequently a sample size of 20 would appear to be too small to give a reasonable chance of finding at least one carrier. This type of calculation can be useful to determine the minimum sample number needed to obtain at least 1 positive result from a sample for any binary variable, e.g. to find at least one affected carrier in a random sample. Flipping a coin can only result in heads or tails. Use this function for quality assurance applications, e.g. to determine the greatest number of defective parts that are allowed to come off an assembly line run without rejecting the entire lot.
Alpha is the criterion value.
Work it out for yourself. In a large field, the chances of putting your finger on a particular blade of grass are millions to one. Consider a statistical analysis of whether banging your head against a hard surface is a cure for the common cold. As soon as 20 studies have been performed, there will be, on average, at least one scientific paper in the Journal of Irreproducible Results proving that banging your head against a wall cures colds. Buy 14,000,000 tickets.