SOLUTION: A person claims to have ESP​ (extrasensory perception). A coin is tossed 30 ​times, and each​ time, the person is asked to predict in advance whether the coin will land heads

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Question 1155291: A person claims to have ESP​ (extrasensory perception). A coin is tossed 30 ​times, and each​ time, the person is asked to predict in advance whether the coin will land heads or tails. The person predicts correctly 60​% of the time​ (i.e., on 18 ​tosses). What is the probability of being correct 18 or more times by pure​ guessing
Answer by ikleyn(52800) About Me  (Show Source):
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It is  P = sum%28C%5B30%5D%5Ek%2A0.6%5Ek%2A0.4%5E%2830-k%29%2Ck=18%2C30%29 = 1 - sum%28C%5B30%5D%5Ek%2A0.6%5Ek%2A0.4%5E%2830-k%29%2Ck=1%2C17%29 = 1 - BINOM.DIST(17,30,0.6,TRUE) = 1 - 0.4215 = 0.5785.    ANSWER


I used the probability 0.6 to guess correctly and 0.4 to guess incorrectly (according to the condition)

Solved.

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I used Excel function BINOM.DIST to quickly calculate the expression.

On Excel function BINOM.DIST, see its description everywhere, for example

https://support.office.com/en-us/article/binom-dist-function-c5ae37b6-f39c-4be2-94c2-509a1480770c