today is the birthday of six (!) of my friends. tomorrow three more, and on friday yet another two. you might wonder what the odds are for two people to have a birthday on the same day? well, let me tell you the answer: it's enough to gather a group of 23 people, and you'll have a 50% chance that any two of them will have a birthday on the same day.
does that seem counter-intuitive? I agree. that's why it's called the birthday paradox. but the maths prove that it is actually true, and a little bit of probabibility theory will do it for you.
we start off by seeing that with 23 people, you can form 23*22/2 = 253 pairs, which is more than half the number of days in a year. (with 28 people you get 378 pairs...) so already there we might suspect something.
to attack the problem, we first start out by finding out what the probability is that for each person we add to the group, that one doesn't have a birthday in common with someone already there. the formula for that is (365 - n)/365 for n being the number of people already in the group (starts out with 0). these separate probabilities are then multiplied, for the n amount of people we want to have. despite each probability being quite high (for n = 23 it's still ~0.9397), multiplying all of these brings the number quite far down, actually all the way to 0.4927, meaning there's a 49.3% chance that our 23rd person doesn't have a birthday already taken. if we then subtract this, we see that we get a 50.7% chance of two people having the same birthdays. done!
if you have 30 people, there's a 70% chance, and with 50 people, you're up to 97% chance to have two people with the same birthday. quite amazing, huh?
in other news, going to the gym is a lot more fun nowadays. a friend of mine suggested that I change the way I do my routines, and pretty much do maximum every time. only 2 sets, and quite few reps. it's a lot more intense, and takes a lot less time. I only do about 3-4 muscle groups, so all in all it's over in about 15-20 minutes. gonna keep this up and do it every day before I leave, and then probably rest a week or so. and then I'll see how it feels, probably going to try and keep it up. it's fun!
does that seem counter-intuitive? I agree. that's why it's called the birthday paradox. but the maths prove that it is actually true, and a little bit of probabibility theory will do it for you.
we start off by seeing that with 23 people, you can form 23*22/2 = 253 pairs, which is more than half the number of days in a year. (with 28 people you get 378 pairs...) so already there we might suspect something.
to attack the problem, we first start out by finding out what the probability is that for each person we add to the group, that one doesn't have a birthday in common with someone already there. the formula for that is (365 - n)/365 for n being the number of people already in the group (starts out with 0). these separate probabilities are then multiplied, for the n amount of people we want to have. despite each probability being quite high (for n = 23 it's still ~0.9397), multiplying all of these brings the number quite far down, actually all the way to 0.4927, meaning there's a 49.3% chance that our 23rd person doesn't have a birthday already taken. if we then subtract this, we see that we get a 50.7% chance of two people having the same birthdays. done!
if you have 30 people, there's a 70% chance, and with 50 people, you're up to 97% chance to have two people with the same birthday. quite amazing, huh?
in other news, going to the gym is a lot more fun nowadays. a friend of mine suggested that I change the way I do my routines, and pretty much do maximum every time. only 2 sets, and quite few reps. it's a lot more intense, and takes a lot less time. I only do about 3-4 muscle groups, so all in all it's over in about 15-20 minutes. gonna keep this up and do it every day before I leave, and then probably rest a week or so. and then I'll see how it feels, probably going to try and keep it up. it's fun!
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