Question

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...Flow chart also.

Answer 1

Answer on Question #45468,

Programming, Mat LAB | Mathematica | MathCAD | Maple

Problem.

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...Flow chart also.

Solution.

Code (MATLAB)

function probability()
    clc();
    % Data for graphic
    peopleArray = [];
    probabilityArray = [];
    % Input
    n = input('The maximal number of people: ');
    m = input('The number of simulations: ');
    for i = 1:1:n
        % The number of successful simulations
        % (when there is two or more people with same birthday date)
        simSuc = 0;
        % Simulation loop
        for j = 1:1:m
            simGrp = randi(365, 1, i);
            if length(unique(simGrp)) ~= i
                simSuc = simSuc + 1;
            end
        end
        % Output
        fprintf('The probability equals %f (%d simulations and %d people)\n', simSuc/m, m, i);
        % Data for graphic
        peopleArray = [peopleArray i];
        probabilityArray = [probabilityArray simSuc/m];
    end
    %Graphic
    plot(peopleArray, probabilityArray)
end

Result

Graphic

Flowchart (http://code2flow.com/abzxt8)