More than 40 times, I've been in a room with more than 30 people & asked them to write their birthdays on paper & hand them to me. Only once were any 2 the same.
Who did this & got significantly different results???
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You have to understand the actual question and the actual results. If you were to ask a group of people, "how large a group would you need for two people to have the same birthday?", you would get answers ranging from several hundred to several thousand.
Some people would understand the situation as having one person with a specific birthday and then would be trying to guess how many people you would need to match that specific birthday.
That's not the question. The question involves any two matching birthdays. Therefore it's a certainty once you invite 366 people since there are only 365 unique days.
The 25 number is when the probability becomes greater than 50% so .51 since it's technically more likely than not at that point. To get to the 99% probability level I think the number is 85 people or something like that.
Another area where people aren't good with properly accessing probability is when someone seems to predict more than it would seem likely that one could predict.
Take a large room of people and ask everyone to answer a random "yes or no" question. Maybe half the room gets it right. Ask just the people who got it right to answer another "yes or no" question. Eventually if you keep going you will end up with just one person and that person will have guessed right maybe 10 times in a row.
That sounds amazing or "beyond coincidence". That person must have ESP right?
Of course not. One person in every room will get more questions in a row correct than everyone else.
It would be amazing if you could predict beforehand who that person would be. It would be amazing if that one person could continue to do this but that's not what is happening.
If you do this "experiment" again, in that same room, someone else will be the "amazing" one.