Mathematics:

The probability that at least two people share their birthday in a room of 23 people approximately 50% This is a pretty famous combinatorial problem, mainly because it is so counter intuitive.

Classic Combinatorial Method: If we were to use the classic combinatorial method to solve this problem, we would start by finding the probability that none of the n people share their birthday. The probability is,

Now, the probability that at least two people share their birthday is,

After some cancellation, the result is,

Monte Carlo Method: First, create several "rooms" with n number of people. Randomly generate their birthday. For simplicity purposes, generating random integer from 1-365 is a good approach. Finally count the number of "rooms" where at least two people shared their birthday. The Monte Carlo Method estimates,

The result is (not always),

Java: importjava.util.ArrayList;importjava.util.Date;importjava.util.HashSet;importjava.util.Random;importo…

The probability that at least two people share their birthday in a room of 23 people approximately 50% This is a pretty famous combinatorial problem, mainly because it is so counter intuitive.

Classic Combinatorial Method: If we were to use the classic combinatorial method to solve this problem, we would start by finding the probability that none of the n people share their birthday. The probability is,

Now, the probability that at least two people share their birthday is,

After some cancellation, the result is,

Monte Carlo Method: First, create several "rooms" with n number of people. Randomly generate their birthday. For simplicity purposes, generating random integer from 1-365 is a good approach. Finally count the number of "rooms" where at least two people shared their birthday. The Monte Carlo Method estimates,

The result is (not always),

Java: importjava.util.ArrayList;importjava.util.Date;importjava.util.HashSet;importjava.util.Random;importo…