Question

HW18 #3

A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 2121 times, and the man is asked to predict the outcome in advance. He gets 1515 out of 2121 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 pp, the chance of success for each individual trial?

Probability of doing at least this well=

Answer 1

Answer:

Given,

sample n = 21

The probability of correct guess = 1/2 = 0.5

i.e., we have two possibilities either right or wrong guesses

p + q = 1

q = 1 - p = 1 - 0.5 = 0.5

p = q = 0.5

Consider,

Binomial distribution P(X = r) = nCr*p^r*q^(n-r)

nCr = n!/(n-r)!*r!

P(X >= 15) = P(15) + P(16) + P(17) + P(18) + P(19) + P(20) + P(21)

= 21C15*0.5^21 + 21C16*0.5^21 + 21C17*0.5^21 + 21C18*0.5^21 + 21C19*0.5^21 + 21C20*0.5^21 + 21C21*0.5^21

= 0.0259 + 0.0097 + 0.0029 + 0.0006 + 0.0001 + 0.00001 + 0.0000005

= 0.0392