Question

You have a friend who claims to psychic. You don't believe this so you test your friend by flipping a coin 20 times and having him predict whether each flip is heads of tails. If you are right, and your friend is NOT psychic, then the probability of guessing correctly on each flip is .5. Your friend correctly guesses 15 out of the 20 flips. What is the probability of your friend correctly guessing 15 or more out of 20 flips if he is NOT really psychic? (Give your answer to at least 3 places past the decimal point)

Answer 1

Answer:

Given that your friend in not really psychic, he has a probability of P=1.5% of guessing right 15 out of 20 coin flips.

Step-by-step explanation:

We have a binomial distribution problem.

We have to calculate the probability of correctly guessing 15 out of 20 flips of a coin (probability of success for every trial: p=0.5).

We can calculate that with the binomial distribution formula:

$P(x)=\frac{n!}{x!(n-x)!}p^x(1-p)^{n-x} \\\\P(15)=\frac{20!}{15!*5!}0.5^{15}*0.5^5\\\\P(15)=15504*0.5^{20}=15504* 0.00000095367 = 0.015$

Then we can conclude that, given that your friend in not really psychic, it has only 1.5% of guessing right 15 out of 20 coin flips.