SOLUTION: A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 22 times, and the man is asked to predict the outcome in advance. He gets 17 out of 22 correc
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Question 1179025: A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 22 times, and the man is asked to predict the outcome in advance. He gets 17 out of 22 correct. What is the probability that he would have done at least this well if he had no ESP?
Probability = Answer by ikleyn(52790) (Show Source):
As I understand, all this variety of unnecessary English words should be filtered out,
and the problem asks ONLY to find the probability of getting 17 or more correct predictions of the total 22 cases.
It is a binomial distribution probability problem.
- number of trials n = 22;
- number of success trials k >= 17;
- Probability of success on a single trial p = 0.5.
We need calculate P(n=22; k>=17; p=0.5).
To facilitate calculations, I use an appropriate online (free of charge) calculator at this web-site
https://stattrek.com/online-calculator/binomial.aspx
It provides nice instructions and a convenient input and output for all relevant options/cases.
P(n=22; k>=17; p=0.5) = 0.00845 (rounded). ANSWER
