A psychic network received telephone calls last year from over 1.5 million people. A recent article attempts to shed some light onto the credibility of the psychic network.
One of the psychic network's psychics agreed to take part in the following experiment.
Five different cards are shuffled, and one is chosen at random. The psychic will then try
to identify which card was drawn without seeing it. Assume that the experiment was
repeated 55 times and that the results of any two experiments are independent of one
another. If we assume that the psychic is a fake (i. e., they are merely guessing at the
cards and have no psychic powers), find the probability that they guess at least three
correctly.
0.999497
0.001917
0.000434
0.000494