A man claims to have extrasensory perception. As a test, a fair coin is flipped 10 times and the man is asked to predict the outcome in advance. He gets 7 out of 10 correct. What is the probability that he would have done at least this well if he had no ESP?

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Lupe Kirkland · Accepted Answer

A man who claims to have extrasensory perception correctly predicted 7 out of 10 coin-flip results. How likely is it that he would have performed at least as well without extrasensory perception? He correctly predicted 7 of the 10 coins, with a probability of 1/2, thus we obviously chose those 7. He was unable to anticipate the results of the following three coin flips with a probability of 1/2 for each. Likewise for 8, 9, or 10 consecutive trials. Let X be the number of following trials.P(X≥7)=(107)⋅1210+(108)⋅1210+(109)⋅1210+(1010)⋅1210=1+10+45+120210=1761024=0.171875The probability of guessing atleast 7 correct flip coins is 0.171875.&amp;nbsp;

A man claims to have extrasensory perception. As a test, a fair coin is flipped

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