Question

A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 26 times, and the man is asked to predict the outcome in advance. He gets 19 out of 26 correct. What is the probability that he would have done at least this well if he had no ESP?

Answer 1

Answer:

0.01448

Step-by-step explanation:

Given that a man claims to have extrasensory perception (ESP).

No of times a fair coin is tossed = 26

No of correct predictions = 19

Let X be the no of correct predictions for x without esp just by mere guess

p = Prob for guess correct = 0.5 and q = 0.5

$P(X\geq 19) = 26C19 (0.5)^{19} (0.5)^{7}+26C19 (0.5)^{20} (0.5)^{6}+...+26C26 (0.5)^{26} (0.5)^{0} \\\\=0.01448$

This will be the probability for getting atleast 19 correct without any ESP