Ronald Fisher is considered the father of experimental design. Being of English descent, he was having afternoon tea with a colleague. The colleague’s wife entered the room as Fisher was pouring tea. Fisher offered tea to the lady. She politely accepted and requested milk with her tea. Fisher started to pour milk into the teacup first, but the lady indicated that she preferred her tea be poured first, then the milk. Fisher did not believe that the lady could tell the difference between “milk first” versus “milk second” tea, but the lady insisted she could tell the difference. Being the consummate scientist, Fisher suggested an experiment in which he randomly put milk into the tea first in some instances and milk into the tea second in others. It turns out, the lady tasting tea was correct in all eight trials.
(a) If we assume that the lady was simply guessing on whether the milk was first or not, what is the probability she would guess correctly on any given cup?
(b) Assuming guessing correctly on one cup is independent of guessing correctly on any other cup, what is the probability of guessing correctly on eight consecutive cups?
(c) Explain how a coin could be used to simulate the random process of tasting eight cups of tea.
(d) Use a coin to simulate Fisher’s experiment at least 2000 times. Based on the simulation, what is the probability of guessing correctly on eight consecutive cups of tea? Compare this result to that of part (b).
(e) What do the probabilities from parts (b) and (d) suggest about the lady tasting tea?