Classic Problems of Probability

Problem 26

Fisher and the Lady Tasting Tea (1935)

Problem. At a tea party, a lady claims she can discriminate by tasting a cup of tea whether the milk (M) or the tea (T) was poured first. To verify her claim, a statistician presents her in random order with eight cups of tea, and tells her there are four of each type M and T. The lady correctly identifies the four M types (and thus also correctly identifies the four T types). How can the statistician verify if her claim is true?

Solution. Consider Table 26.1, which shows the lady's response in the tea-tasting experiment.

Table 26.1 The Lady's Response in Fisher's Tea-Tasting Experiment.

Conditional on the true states T and M, suppose the lady responds T with probabilities and , respectively. The lady's claim is false if , that is, the odds ratio . Under the null hypothesis , the probability of correctly answering T for each of the four ...