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 45 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.
A) 0.003141
B) 0.009657
C) 0.996771
D) 0.002695

Question

Quizplus · Accepted Answer

The probability of guessing a card correctly is 1/5, and incorrectly is 4/5. The probability of guessing at least 3 cards correctly out of 45 can be found using the binomial distribution formula or complementary probability (1 - probability of guessing 0, 1, or 2 cards correctly). Calculating or approximating this probability gives a value close to 0.996771, indicating a high likelihood of guessing at least 3 cards correctly by chance over 45 trials.

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