Testing a psychic’s ability. Consider an experiment in which 10 identical small boxes are placed side by side on a table. A crystal is placed at random inside one of the boxes. A self-professed “psychic” is asked to pick the box that contains the crystal.
a. If the “psychic” simply guesses, what is the probability that she picks the box with the crystal?
b. If the experiment is repeated seven times, what is the probability that the “psychic” guesses correctly at least once?
c. A group called the Tampa Bay Skeptics recently tested a self-proclaimed “psychic” by administering the preceding experiment seven times. The “psychic” failed to pick the correct box all seven times (Tampa Tribune, Sept. 20, 1998). What would you infer about this person’s psychic ability?
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