Question

A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 23 23 times, and the man is asked to predict the outcome in advance. He gets 18 18 out of 23 23 correct. What is the probability that he would have done at least this well if he had no ESP?

Answer 1

the probability that he can predict the outcome write when a fair coin is tossed is 0.5 ( as there is only two outcome Head and Tail)

The total number of toss: n= 23

this can be done using the binomial probability distribution.

with the probability of success: p= 0.5

total number of trials: n= 23

the probability that he would have done at least this well if he had no ESP= the probability to correctly guess 18 out of 23 correct is

=

P(X > 18)1- P(X < 18)

17 P(X < 18) Σ PC(0.5)"(1-05)23-r = 0.9947

=

P(X > 18)-1-0.9947= 0.0053

the probability that he would have done at least this well if he had no ESP= 0.0053