A psychic network received telephone calls last year from over 1.5 million people. A recent article attempts toshed some light onto the credibility of the psychic network. One of the psychic networkʹs psychics agreed totake part in the following experiment. Five different cards are shuffled, and one is chosen at random. Thepsychic will then try to identify which card was drawn without seeing it. Assume that the experiment wasrepeated 50 times and that the results of any two experiments are independent of one another. If we assumethat the psychic is a fake (i.e., they are merely guessing at the cards and have no psychic powers), find theprobability that they guess at least three correctly.
A) 0.998715
B) 0.001257
C) 0.004371
D) 0.001093

Question

Quizplus · Accepted Answer

The probability of guessing a card correctly is 1/5, and incorrectly is 4/5. To find the probability of guessing at least 3 cards correctly out of 50, we use the binomial distribution formula. However, calculating the probability directly for 3 to 50 correct guesses is cumbersome. Instead, it's easier to calculate the probability of guessing 0, 1, or 2 cards correctly and subtracting from 1. The result is very close to 1, indicating a high probability of guessing at least 3 cards correctly by chance, which aligns with choice A.

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