Question

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 1616 out of 2121 correct. What is the probability that he would have done at least this well if he had no ESP?

Answer 1

n = 21, x = 16

If the man had no ESP, then his chance of a correct call on every flip would have been p = 1/2

q = 1 - p = 1/2

We want the probability that he would get at least 16 calls correct out of 21

Using binomial distribution, we want to find P(x ≥ 16)

x	P(x) = C(21, x) (1/2)^x (1/2)^(21 - x)
0	0
1	0
2	0.000100136
3	0.000634193
4	0.00285387
5	0.009703159
6	0.025875092
7	0.055446625
8	0.097031593
9	0.140156746
10	0.168188095
11	0.168188095
12	0.140156746
13	0.097031593
14	0.055446625
15	0.025875092
16	0.009703159
17	0.00285387
18	0.000634193
19	0.000100136
20	0
21	0

P(x ≥ 16) = P(16) + P(17) + P(18) + P(19) + P(20) + P(21) = 0.0133

Answer: 0.0133