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?

A man

hansel

Answered by Aaron 3 years ago

If he does *at least this well* then he will get 7 out of 10 correct or 8, 9 or 10 out of 10 correct. So in the case where we have a certain probability of success or failure we use the binomial theorem and get the following,

$$C(10,7)(1/2)^7(1/2)^3 + C(10,8)(1/2)^8(1/2)^2+C(10,9)(1/2)^9(1/2)^1+C(10,10)(1/2)^{10}(1/2)^0$$

$$\approx 0.1719$$

or he has a 17.19% probability of doing at least that well.

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Asked: 3 years ago