Question

A person claims to have ESP​ (extrasensory perception). A coin is tossed 28 times, and each​ time, the person is asked to predict in advance whether the coin will land heads or tails. The person predicts correctly 64% of the time​ (i.e., on 18 tosses). What is the probability of being correct 18 or more times by pure​ guessing?

Answer 1

This a problem for binomial distribution where n = 28, p =0.5 (since the person would now be guessing)

Probabaility of being 18 or more times correct out of 28, is as follows

P(18<=X<=28) = 1- P(X<=17)

P(X<=17) is P(X=0)+ P(X=1)+.....+P(X=17)

Thus we need to obtain the cumulative probabilities for P(X<=17)

Using the cumulative probability table at n=28, x=17 and p=0.5. (We can also use the pbinom(17,28,0.5) function in R )

P(X<=17) =0.9075

P(18<=X<=288) = 1- P(X<=17) = 1 - 0.9075 =0.0925

Thus the probability of being correct 18 or more times out of 28, by pure guessing is 0.0925