It’s Your Birthday
… Want an Easy Bet?
Well they say that should never take a bet from someone who says “I’ll bet you …”. So let’s take an easy bet for you…
If we have classes of 30 students, and I take the money if there is at least two students in the class with the same birthday, otherwise you can have the money.
Do you take the bet? Surely it’s 1-in-365, or perhaps it’s 30-in-365 (less than a one-in-ten chance that I will win) ? Either way you win at least 10 times more than me. It looks a great bet, and you surely can’t lose.
Unfortunately for you, this is the classic Birthday problem, and its a bad bet, as there is a greater than 70% chance that I will win each time:
http://asecuritysite.com/encryption/birthday?val=365,30
If fact if we take a class of 60, there is 99.4% chance of me winning. So if we sampled 1,000 classes, I would win 994 times and you would win just six times … not a good bet!
If you are interested the equation is:
The 365! part stands for 365x364x364…x2x1.
So I reckon that a fair bet is with classes of 23 students, and we both have roughly an evens chance of winning. Here are the estimates:
- Same birthday with 1 person should give 0%. Calc
