# If a hypothesis confers a low probability on an observation, is this evidence against the hypothesis?

Intuitively, it seems yes. However, the more I think about it, it seems no, even though this goes against my intuition.

Imagine if all that the universe consisted of was one game where you won a prize of a million dollars. Let's call this scenario A. The chance of winning was 1 in a million. Now, suppose there is only one person who plays it and he wins.

Now imagine if all that the universe consisted of was this one game but a million people played it. Let's call this scenario B. Now, suppose one of out these people wins.

Intuitively, it seems that it is more likely for scenario A to involve cheating than scenario B. But is this solely because the first scenario has a lower probability of happening by chance or is it because the probability of it being cheated with is higher than the former probability?

What if, say, there was no known way to cheat these games. The games had been rigorously tested and there was simply no known natural way to interfere with these games. What then?

• Just don't rely on intuition, which has been shown time and again to be misleading. Commented Jan 17, 2023 at 1:06
• Scenario A is indeed more likely to be due to cheating. However, although it makes cheating more probable it does not exclude the possibility of a fair win. This situation should just lead you to investigate further, whichever what you propose in the last paragraph. Now, "no known way to cheat" still does not proof beyond any doubt that the winner didn't cheat. An actual evidence that the winner did cheat would be decisive. Commented Jan 17, 2023 at 3:37
• @armand Well, let me put it this way. There is also no known way for a supernatural being to intervene in affairs. However, scenario A would not prove beyond any doubt that the supernatural being didn't intervene. Would this mean it is more likely there was supernatural intervention in scenario A than B?
– user62907
Commented Jan 17, 2023 at 3:41
• It depends on your acceptance of supernatural intervention in the first place. If you don't believe in the supernatural, then the probability it influenced the game is zero in both cases. Commented Jan 17, 2023 at 3:46
• @armand Then that begs the question: what should your acceptance be? Also, shouldn't your acceptance be based on the data rather than the other way around? If so, then enough data should turn a non acceptance into acceptance
– user62907
Commented Jan 17, 2023 at 4:13