The Birthday Paradox

published on July 13, 2020

Vsauce Kevin here I've got 23 babies which means there's a 50% chance one of them can hack one of the others and replace their DNA wait humans can't hack each other yet but computers can't and luckily for us it turns out that the fine folks at

BitDefender are big fans of Vsauce 2 and I'll get into the ways that BitDefender is a great solution for protecting your device's like most people know that open Wi-Fi connections aren't safe but why exactly and how can you get hacked for

Connecting to public unsecured Wi-Fi but first what do hacking and babies have in common birthdays let me explain each one of these babies has a random birthday meaning that they each have the same

Chance of having been born on any one of the 365 days in a year so what are the odds that two of them share the same birthday we'll keep it simple no twins no leap years no patterns that suggested parents made their babies at non-random

Specific times the odds aren't 23 out of 365 which would be about 6 percent the odds are actually 50% there's a 50% chance that out of 23 random people to have the same exact birthday which seems impossible given that we've got so few

Babies and so many possible birthdays and if we have 50 babies the odds of a birthday match jump up to 97 percent at 75 it's 9997% making it a virtual certainty that when you get 75 babies together or 75 things with birthdays

They don't have to be babies two of them will share a birthday the birthday paradox is a vertical paradox it's surprising and absurd sounding but we have the math to prove it's true how is it possible that

So few babies can have such a high chance of sharing a birthday and how is it that despite 365 possibilities we only need a sixth of that number to be pretty sure there's a match the easiest way to do this isn't to excuse me babies

Babies oh geez oh geez babies raising babies alright that's not good the easiest way to do this isn't to calculate the probability that – of any number of babies share the same birthday it's to calculate the probability that

They don't to do that we assume that baby number 1 has been born so the probability of this baby having a birthday is 1 or 365 over 365 then we multiply that by baby number two's probability of not sharing that birthday

364 over 365 we multiply that result by baby number three's probability of not sharing a birthday with either baby number one or baby number two which is 363 over 365 and we keep doing this for as many babies as we want to calculate

The odds for at baby 23 were multiplying by 343 over 365 to simplify this calculation we can write it as 364 factorial will start with 364 because 365 over 365 is just 1 over 342 factorial because 365 minus our 23

Babies gives us 342 times 365 days out of the air raised to the 22nd power which is our 23 babies – baby 1 again ok and the result of the whole equation gives us 049 – 703 or about 493%

Again that's the probability we don't have a birthday match with 23 babies so we subtract this from 1 to find the chance that we do which is 05 0 7 297 which is about 507% the trick here is that every baby is being evaluated

Against each other and actually broke my pen trying to make all these evaluation lines it's it's not whether babies 2 through 23 share a birthday with just baby one to have a 50% chance of a match with a single predefined birthday like

Like a 50% chance of finding a match with baby number five specific birthday we need a pool of 253 babies which sounds about right and isn't particularly surprising this is whether any two babies share any birthday with

One another the high probability 50% with a low baby count 23 is surprising but the math works and if we keep extending this series the results show that with 100 babies fewer than a third of the possible birthdays in a given

Year the chances of a match are 999999 7 percent which means the chances of not having a birthday overlap would be just point 0 0 0 0 3 percent or 3 in 10,000,000 if we replace our birthday babies with

Online passwords we've got the basis for a type of hack known as the birthday attack when you make a password for a website that password is crunched into a fixed length hash value that stores and identifies the combination of characters

You input so like 1 2 3 4 5 becomes 8 – 7 c CB 0 e e a8 a 7 0 6 C 4 C 3 4 a 1 6 8 9 1 F 847 B simple when the md5 message digests algorithm is a standard for encryption it's 128 bit 32 hexadecimal hashes were

Vulnerable to a hack based on my babies the goal was to find and force a collision when two hashes have the same exact value regardless of what that value is so like if Vsauce 2 dot doc and Kevin dot doc had the same hash value I

Could change information in one and affect the other or I could eventually use collisions like this to decode the encryption algorithm itself and learn how it works and the best way to do this wasn't a trial and error or brute-force

Attempt to guess a specific match in the 34 times 10 to the 38th possible outcomes it was putting the birthday paradox to use hackers developed an algorithm based on the math of the birthday paradox to more quickly cause

Hash collisions and ultimately crack one of the most widely used cryptographic algorithms of its time so probabilities surrounding birthdays helped lead to the improvement of internet security and right now online

As long as 70 people are watching this video at the same time there's a 999% chance two of you blow out your birthday candles on the same day of the year so when were you born and as always thanks for watching

okay now here's how you can get hacked by connecting to open Wi-Fi whenever you connect to a Wi-Fi network your phone or laptop will remember it and then automatically connect to it when in

Range now if you only connect it to secured Wi-Fi networks you're fine if however you connect it to just one open Wi-Fi in your devices history an attacker will have an easy time hijacking your device all Wi-Fi enabled

Devices when not connected constantly broadcast their known Wi-Fi access point list basically they keep shouting is Starbucks here is McDonald's here is the airport here and so on attackers can listen for these

Broadcasts and then once they see their target asking for something that looks like an open Wi-Fi they just create a new one with that same name all the devices that have that name in their memory will then automatically connect

To the attackers imposter Wi-Fi and once you're connected to their Wi-Fi the attackers are inside a device so first of all don't do that to other people don't be an attacker and second of all stop cyberattacks before they begin by

Protecting all of your privacy data and devices with bitdefender's award-winning 20:19 Security Suite which includes BitDefender VPN to protect you from those open Wi-Fi attacks trusted by over 500 million users and for a limited time

For new users in the US and Canada they're offering your first six months for free six months half a year of cyber security for free so find the link below to get yours right now it's free six months for free so

Click that click that down there and thank you BitDefender for supporting vsauce2 and my birthday babies

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