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Suppose you are a board game maker, and you want to give players a higher probab

ID: 3792437 • Letter: S

Question

Suppose you are a board game maker, and you want to give players a higher probability of rolling larger numbers. Originally you had them roll three six-sided dice and add their results. The new approach will have the player roll four dice and add the totals of the three highest valued dice. Write a program that counts through every permutation of four six-sided dice and find the total of the three highest valued dice. Calculate the permutations of rolling four six-sided dice Plot a histogram of the totals Calculate the mean and standard deviation of the totals Plot a histogram of the values for the lowest valued, second-lowest, third-lowest, and highest value dice

Explanation / Answer

function prob=sumDicePDF(n,k)

    if n < 1 || k < n || k > 6*n

        display('Bad Input! Try Again.');

        n = input('n = ');

        k = input('k = ');

        prob=sumDicePDF(n,k);

        return;

    end

    %If there is only one dice return probability 1/6

    if n == 1

        prob = 1/6;

        return;

    end

      valuesMatix = zeros(n - 1,6*n); %Define new matrix size n-1,n*6

                                       %with zeros

      for i = 1:6

          valuesMatix(1,i) = 1/6;

      end

      for i = 2:n - 1

          for j = i:6*i              

              probForSpecPlace = 0;

              for l = 1:6

                  if j - l > 0 %Check if value out of range becouse

                      probForSpecPlace = probForSpecPlace + valuesMatix(i - 1,j - l)*1/6;

                  end

              end

              valuesMatix(i,j) = probForSpecPlace;              

          end

      end

      prob = 0; %Define the probability to 0

      for i = 1:6

          if k - i > 0

              prob = prob + valuesMatix(n - 1,k - i)*1/6;

          end

      end

end