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【奶茶與費雪】

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Humans are really terrible at guessing probabilities:

https://mathwithbaddrawings.com/2018/07/11/why-its-so-hard-to-surprise-a-mathematician/

One way I like to think about the 'Birthday-Paradox' is to consider three cases:

[1] "What are the chances that in a room of 23 people some person picked at random has the same birthday as another person in the room?"

[2] "What are the chances that in a room of 23 people two of the folks in the room have the same birthday?"

[3] "What are the chances that in a room of 23 people two of the folks in the room were born on the same date?"

When we read the three questions they seem to be very simular but are instead different. And, since only ONE of the questions is the "Birthday-Paradox", and we clump all of them together we are surprised that one of the questions has a much higher probability than the other two.

[1] The chances of this occurring are VERY SMALL (6%)

[2] The chances of this occurring are VERY GOOD (over 50%) - This IS the "Birthday Paradox".

[3] We conflate "date of birth" with day of the year you celebrate the anniversary of your birth. Your date of birth includes the year you were born. The anniversary of your birth ignores the year you were born.

The chances of this occurring depend on THE GROUP. This question turns into [2] when you consider a group like a class in a school since everyone was most likely born in the same year so you can ignore the year.

And if you just pick people at random from the general population the chances go way, way down since you get many different years of birth.
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I've read about this result before but the explanation in the video goes much deeper than any explanation I seen so far. An excellent video. (And it is a bit too long to fit in the margin of a piece of paper :)
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M77232917 is the new largest known prime number, which is 23 million digits long.
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#數學史
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