Question

A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 29 times, and the man is asked to predict the outcome in advance. He gets 25 out of 29 correct. What is the probability that he would have done at least this well if he had no ESP? Hint: If he has no ESP, then he's just randomly guessing, right- If he is randomly guessing, what should you use as p, the chance of success for each individual trial? Probability of doing at least this well =

Answer 1

We can model this event as binomial here is to be right.

p = 0.5

Assume the person says the heads will appear. P(heads) = 0.5 since 1 of two equally likely outcomes. So person's chance of being right would be linked to the outcome.

There are 29 flips : n = 29

To be at least this well means to be correct at 25 times out of 29.

At least 25 means 25 or more So

(n = 29 ,p = 0.5 )

P( X =x) =

=

=

P(X >= 25) = P(X = 25) + P( X = 26) + P(X = 27) + P( X = 28) + P( X = 29)

= 0.000044 + 0.000007 + 0.000001 + 0.00 + 000

Ans: 0.000052

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