May 23, 2022

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A simulation of the 'Christmas Paradox' teaches us that humans are not very good at estimating probabilities

A simulation of the ‘Christmas Paradox’ teaches us that humans are not very good at estimating probabilities

to Tweet embed – May 2, 2022

To present the known file Christmas paradox The people gathered in class are usually made up of how many people are there – maybe 30 or 40 – and that a year has 365 days. Then he asks if they think it’s possible Two people have the same birthday; You may also be asked to estimate how many people it will take for the probability of this to happen to be more than 50%. With so many – but it doesn’t have to be huge either – there are those who even suggest betting real money, knowing that they have the laws of probability in their favour, as some accounts show.

Which is that this effect is called a paradox because the result It doesn’t make sense: just need 23 people in a group So that the probability is more than 50%. The key is that the problem is asking “two people have the same birthday”, not that one person’s birthday is the same as someone else’s. specific. In the first case, 23 people can make 253 different pairs, and they are all candidates. If we were referring to just one person in particular, it would be 1/365 for each of the 22 people, (22/365) = 6% in total, which is much less. (Note: It is usually ignored leap years.)

To make it look more clear Brain feast Turn it all into a file Birthday Paradox Simulator In the module, where there are buttons to press and modify certain variables:

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You can increase or decrease The number of people (People) In each room, clicking room generation (generating room) Dates are chosen for all people, with a number between 1 and 365 symbolizing each day of the year.

As a result, the file Colors Indicate whether the dates do not repeat (red) or coincide (green); In fact, sometimes more than one pair matches. The most interesting thing is that you can Generate random samples 10 to 10, 100 to 100 or in multiples of 10 (button samples) for faster testing. The lower right panels aggregate and average the scores so you can see how important the stats are as they evolve (in the simulation this is explained as “number of rooms visited”).

Increase the number of people in the room It’s easy to see how difficult it gets Avoids That the two dates coincide. In the specific case in a room of 365 people, it would be practically impossible not to have a coincidence, since each person would have to be born on a completely different day of the year.

In addition to checking how famous the value 23 It is numerically accurate in the case of birthdays to overcome the 50% barrier (specifically the probability is 50.7%; in the case of only 22 people it is only 47.6%) The most important thing about this paradox is Find out how to recognize him in other situations. Once internalized, many of those “amazing coincidences” that we observe in our daily lives are no longer so, because the number of “possible coincidences” is so great that sometimes they are more likely than unexpected events.

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