A common test for extrasensory perception (ESP) asks subjects to identify which of four shapes (star, circle, wave, or square) appears on a card unseen by the subject. Consider a test of n = 40 trials, where you will count how many times the subject specifies the correct shape. Suppose you want to determine if Chris has ESP. Let p = probability of a correct answer for Chris (that is, the proportion of correct responses if we tested Chris forever).
If Chris does not have ESP and is just guessing, what is the value for p? What is the probability he gets more than 30 correct out of 40 trials?