Question

(1 point) A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 28 times, and the man is asked to predict the outcome in advance. He gets 20 out of 28 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 p, the chance of success for each individual trial?

Probability of doing at least this well =

Answer 1

Answer)

As there are fixed number of trials and probability of each and every trial is same and independent of each other

Here we need to use the binomial formula

P(r) = ncr*(p^r)*(1-p)^n-r

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

N! = N*n-1*n-2*n-3*n-4*n-5........till 1

For example 5! = 5*4*3*2*1

Special case is 0! = 1

P = probability of single trial = 0.5 {since there are two total outcomes and one favorable, p = 1/2 = 0.5}

N = number of trials = 28

R = desired success = greater than or equal to 20

P(20) + P(21) + ..... + p(27) + p(28)

= 0.01784906909