Testing a psychic’s ESP. Refer to Exercise 3.101

(p. 186)

and the experiment conducted by the Tampa Bay Skeptics to see whether an acclaimed psychic has extrasensory perception

(ESP). Recall that a crystal was placed, at random, inside 1 of 10 identical boxes lying side by side on a table.

The experiment was repeated seven times, and x, the number of correct decisions, was recorded. (Assume that the seven trials are independent.)

a. If the psychic is guessing (i.e., if the psychic does not possess ESP), what is the value of p, the probability of a correct decision on each trial?

b. If the psychic is guessing, what is the expected number of correct decisions in seven trials?

c. If the psychic is guessing, what is the probability of no correct decisions in seven trials?

d. Now suppose the psychic has ESP and p = .5. What is the probability that the psychic guesses incorrectly in all seven trials?

e. Refer to part

d. Recall that the psychic failed to select the box with the crystal on all seven trials. Is this evidence against the psychic having ESP? Explain.