A classic study of extrasensory perception tests the ability of one person to read another's mind. The test uses five cards with different designs, all known to both participants. In each trial, the "sender" sees a randomly chosen card and concentrates on its design. The "receiver" guesses the identity of the card. Each of the five cards is equally likely to be chosen.
a. In a series of 40 trials, the receiver identified 12 cards correctly. What is her rate of success? What rate of success is expected, assuming she is only guessing?
b. Test the hypothesis that the receiver is telepathic (i.e., she has a higher rate of success than expected).