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

Answer 1

Answer on Question #45298,

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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 $n = 2,3,4\ldots$ 40

Solution.

Code (MATLAB)

function probability()
    clc();
    % Input
    n = input('Enter the number of people:');
    m = input('Enter the number simulation:');
    % The number of case in which two or more have the same birthday
    success = 0;
    % Loop to compute success
    for i = 1:1:m
        group = randi(365,1,n);
        if length(unique(group)) == n
            success = success + 1;
        end
    end
    % Output
    fprintf('The probability equals %f\n', success/m);
end

Result

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