Answer:
2.16% probability that he would have done at least this well if he had no ESP
Explanation:
For each coin toss, there are only two possible outcomes. Either he predicts the correct outcome, or he does not. The tosses are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.
Fair coin:
Equally as likely to be heads or tails, so
Coin is flipped 25 times
So

What is the probability that he would have done at least this well if he had no ESP?

In which






The others(23, 24 and 25) are close to 0.

2.16% probability that he would have done at least this well if he had no ESP