Question

A man claims to have extrasensory perception. As a test, a fair coin is flipped 10 times and the man is asked to pick the outcome in advance. (‘Fair’ means here that heads and tails are equally likely.) He gets 7 correct. What is the probability he would have done just as well (that is guessed 7 or more correctly) by randomly guessing?

Answer 1

0.9375

Explanation:

Given that a man claims to have extrasensory perception. As a test, a fair coin is flipped 10 times and the man is asked to pick the outcome in advance. (‘Fair’ means here that heads and tails are equally likely.) He gets 7 correct.

Suppose he has done only by guessing then probability would be:

Let X be no of head obtained by tossing a coin 10 times

X is binomial because each trial is independent and probability is 0.5

Reqd probability

= P(X=7) =
`10C7(0.5)^7\\\\= =0.9375`

The probability he would have done just as well (that is guessed 7 or more correctly) by randomly guessing is 0.9375