Question

A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 23 times, and the man is asked to predict the outcome in advance. He gets 20 out of 23 correct. What is the probability that he would have done at least this well if he had no ESP

Answer 1

The probability that he would have done at least this well if he had no ESP is 0.99979

What is the probability of determining that he would have done well with no ESP?

To determine the probability, we need to first find the probability of doing well with ESP.

The probability of having 20 correct answers out of 23 coin flips is:

$\mathbf{=(\dfrac{1}{2})^{20}}$

Since we have 20 correct answers, we also need to find the probability of getting 3 answers wrong, which is:

$\mathbf{=(\dfrac{1}{2})^{3}}$

There are $(^{23}_{20})$ = 1771 ways to get 20 correct answers out of 23.

Therefore, the probability of doing well with ESP is:

$\mathbf{= 1771 \times (\dfrac{1}{2})^{20}} \times (\dfrac{1}{2})^{3}}$

= 0.00021

The probability that he would have at least done well if he had no ESP is:

= 1 - 0.00021

= 0.99979

Learn more about probability here:

brainly.com/question/24756209

#SPJ1