Question

We have seen that the probability that at least two people in a group of 23 people share the same birthday is approximately 0.5. In this question we are interested in the probability that at least three people in a group of 23 people share the same birthday. Draw 23 numbers independently from the integers {1, 2, . . . , 365} with each number equally likely to be drawn. Let E be the event that at least one of the integers 1, 2, . . . , 365 appears three or more times among the 23 drawn numbers. Simulate this process 10000 times in MATLAB to give an estimate of the probability that the event E occurs. Submit your estimate together with the MATLAB code you used to get this estimate. [2] (You may find the functions randi, tabulate and mean in MATLAB helpful.)

Answer 1

FROM GIVEN DATA:

• %Matlab code for finding probability of 3 people among 23 people sharing
  %same birthday
  clear all
  close all
  %finding random numbers between 1 and 365
  a=1;
  b=365;
  count=0;
  %total number of drawns 10000 times
  for i=1:10000
      A = randi([a b],1,23);

      %checking if atleast one of the integers appears three or more times
      B = unique(A); % which will give you the unique elements of A in array B
      Ncount = histc(A, B); %
      tf=sum(Ncount>=3);
      if tf>=1
          count=count+1;
      end
    
  end

• probability= (count/10000);

  fprintf('Hence the probability at least three people sharing same birthday among 23 people is %f.\n',probability)

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