Answer to Question #45329 in MatLAB | Mathematica | MathCAD | Maple for Akshay Joshi

Question

The Birthday Problem: The birthday problem is stated as follows:
If there is a group of n people in a room, what is the probability that two or more of them having same
birthday? It is possible to determine answer to this question by simulation. (Hint: You can generate
random dates, n times and determine the fraction of people who born in a given day). Write a function
that determines the answer to this question by simulation. The program you write can take n as the
input and prints out the probability that two or more of n people will have the same birthday for
n=2,3,4…. 40

Answer 1

close all; clear all; clc;
date_min = datenum([1960 1 1]);             % start date
date_max = floor(now);                      % current date
N = 40;
P = zeros(1,N-1);
for n=2:N
   date_r = randi([date_min date_max], 1, n);     % random day
       date_r_d = datevec(date_r);             
       d = date_r_d(:,3);
       m = date_r_d(:,2);
        c = 0;
       for i = 1:n
            for j = 1:n
                if m(i) == m(j) && d(i) == d(j) && i ~= j
                    c = c + 1;
                end
            end
        end
        P(n-1) = c/n;
end
P