Question

A coin is tossed 20 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 16 tosses. What is the probability of being correct 16 or more times by guessing? Does this probability seem to verify her claim?

Answer 1

No, the probability doesn't seem to verify the claim as it is greater than 0.5.

Explanation:

Given information:

Let X be the number of times the person predicts correctly about the outcome of a coin and follows a binomial distribution.

The probability (p) that the person predicts correctly about the outcome of a coin is 16/20.

Now, the probability of being correct 16 or more times by guessing is calculated below:

`P(X\geq 16)= P(X=16)+ P(X=17)+ P(X=18)+ P(X=19)+P(X=20)`

=
`{^20}C_16`
`\left((16)/(20)\right)^(16)}* \left(1-(16)/(20)\right)^(20-16)` +

`{^20}C_17`
`\left((16)/(20)\right)^(17)}* \left(1-(16)/(20)\right)^(20-17)`+.......+

`{^20}C_20`
`\left((16)/(20)\right)^(20)*\left(1-(16)/(20)\right)`

= 0.6296

Hence, the probability doesn't seem to verify the claim as it is greater than 0.5.