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

Question

2 years ago

6

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

1 answer:

77julia77 [94] · Answer 1 · 2023-09-05T04:18:20+03:00

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

<h3>What is the probability of determining that he would have done well with no ESP?</h3>

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:

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