Question

A coin is tossed 20 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 14 tosses. What is the probability of being correct 14 or more times by guessing? Does this probability seem to verify her claim?

Answer 1

The experiment could be considered as a Bernoulli trial, modeled by the Binomial distribution.

n = 20, number of trials
p = 1/2, the probability of success
q = 1-p = 1/2, probability of failure

The probability of at least 14 successes in 20 trial is
P(success>=14) = ₂₀C₁₄ p¹⁴ q²⁰⁻¹⁴
  $= \frac{20!}{6!14!} ( \frac{1}{2} )^{14}( \frac{1}{2})^{6}$
$= \frac{20.19.18.17.16.15.14!}{6.5.4.3.2.14!} ( \frac{1}{2})^{20}$
= 0.037

Answer: 0.037
This answer is plausible.