Finding a psychic ability

I am a bit confused by the problem that is in the Statistics Fundamentals Course, Chapter 1 (Statistics Introduction), Lesson 3 Deception.

A study is done on 250 people who claim they have psychic abilities. A regular deck of cards has an equal number of red and black cards. The deck is shuffled, and each person predicts the color of the top card. The top card is then flipped face up to see if they are correct. This is repeated 8 times in a row. One participant gets all 8 predictions correct! The researcher claims that this person has exhibited psychic abilities. Based on just the way the experiment is designed, is the researcher's claim a viable hypothesis? (Note: we're not judging the plausibility of psychic ability in itself, just this particular experiment's design.)

Explanation Correct answer: No

If someone guesses randomly between two equally-likely options, we would expect them to make all 8 guesses correct with a probability of ( $\frac{1}{2}$ )^2= $\frac{1}{256}$ .

Given there are nearly 256 people in the experiment, it is reasonable to expect at least one of them would get all 8 correct by random chance. Therefore, the experiment as designed suggests nothing about psychic ability.

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Is it right that a proposed solution is correct if every participant provides a unique combination? As far as I understand since every combination proposed by a participant is an independent occasion (so they can be duplicated), we also need to multiply $\frac{1}{256}$ by $\frac{1}{250}$ . Thus, it will give us a $\frac{1}{64000}$ chance that someone will guess the right combination.