The Lady Tasting Tea is one of the most famous experiments in the founding history of statistics. In his 1935 book The Design of Experiments (1935), Sir Ronald A. Fisher writes, A Lady declares that by tasting a cup of tea made with milk she can discriminate whether the milk or the tea infusion was first added to the cup. We will consider the problem of designing an experiment by means of which this assertion can be tested . . . Our experiment consists in mixing eight cups of tea, four in one way and four in the other, and presenting them to the subject for judgment in a random order. . . . Her task is to divide the 8 cups into two sets of 4, agreeing, if possible, with the treatments received. Consider such an experiment. Four cups are poured milk first and four cups are poured tea first and presented to a friend for tasting. Let X be the number of milk-first cups that your friend correctly identifies as milk-first.

(a) Identify the distribution of X.
(b) Find P(X = k) for k = 0, 1, 2, 3, 4.
(c) If in reality your friend had no ability to discriminate and actually guessed, what is the probability they would correctly identify all four cups correctly?