The replication of an experiment

Summary

The importance of replicating an experiment is shown by the consideration of the following problem:—To find out the nature of the coins in a set of 12 from merely the results of throws. The case discussed is the simplest in which each throw is assumed to have given the same result, namely 4 heads and 8 tails. It is shown that, in general, each throw increases, but never decreases, the accuracy of our result. It is also seen that after 11 experiments (throws) our knowledge of the set becomes complete and thus further experiments become unnecessary when the limit for random chance assumed by us is 5%.