A man claims to have extrasensory perception. As a test, a fair coin is flipped 28 times, and the man is asked to predict the outcome in advance. He gets 25 out of 28 correct. What is the probability that he would have done at least this well if he had no ESP?

Using the probability mass function we got:

And adding the probabilities we got:

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".  

Let X the random variable of interest, on this case we now that:  

The probability mass function for the Binomial distribution is given as:  

Where (nCx) means combinatory and it's given by this formula:  

Solution to the problem

For a fair coin flip n=28 times we have the following distribution:

We want to find this probability:

Using the probability mass function we got:

And adding the probabilities we got:

step-by-step explanation:

given expression is .

now we need to simplify the given expression .

we know that square root is equivalent to the power 1/2. so that means we can take half of the exponents to get the square root of given expression.

expanding that will give a very very large number so let's keep answer in exponent form.