Compute Probabilities of Binomial Experiments
-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 15 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) 0.601977
B) 0.327654
C) 0.250139
D) 0.230897

Question

Quizplus · Accepted Answer

The probability of guessing at least three cards correctly in 15 trials, assuming the psychic is guessing (success probability = 1/5), can be calculated using the binomial distribution formula or a binomial probability calculator. The complement approach (1 - probability of guessing 0, 1, or 2 correctly) is often easier for "at least" problems. Calculating directly or using a calculator for "at least 3" successes out of 15 trials with a success probability of 0.2 (1/5) gives a probability of approximately 0.601977.