Question

Consider tossing two dice with faces labelled 1, 2 and 3. (a) What is the probability distribution of the sum of the values? (b) Use Matlab to simulate the tossing of these 2 dice for 10,000 times. Plot the histogram of the sum face values. From the simulation, estimate the probability of the sum face values in part (a). (Hint: use the function randi() to simulate pseudorandom integers.)

Answer 1

(a)

There are 2 die with faces labelled 1, 2 and 3
Total possible combinations of tossing 2 die = 3*3 = 9
Possible sum obtained by tossing 2 die : {2,3,4,5,6}
Total possible combinations of obtaining sum 2 : {{1,1}} = 1/9
Total possible combinations of obtaining sum 3 : {{1,2},{2,1}} = 2/9
Total possible combinations of obtaining sum 4 : {{2,2},{1,3},{3,1}} = 3/9
Total possible combinations of obtaining sum 5 : {{2,3},{3,2}} = 2/9
Total possible combinations of obtaining sum 6 : {{3,3}} = 1/9

Probability distribution is P(x):
   1/9 , if x={2,6}
   2/9 , if x={3,5}
   3/9 , if x={4}
  

(b)

% Matlab script to simulate the tossing of 2 dice(3 sided) for 10,000 times
% Plot the histogram of the sum face values.
% From the simulation, estimate the probability of the sum face values

% get the result of sum of simulating 2 3-sided die 10,000 times
rolling_2_dice_sum = randi([1,3],1,10000)+randi([1,3],1,10000);
% vector to contain the frequency of occurence of the each possible sum
count_sum_face_values = zeros(1,5);
% loop to get the number of times each sum occurs
for i=1:length(rolling_2_dice_sum)
count_sum_face_values(rolling_2_dice_sum(i)-1)= count_sum_face_values(rolling_2_dice_sum(i)-1) + 1;
end
% calculate the probability distribution of the sum face values
probability_dist = count_sum_face_values ./ sum(count_sum_face_values);
% output the probability distribution of the sum face values
fprintf('Probability distribution :\n%10s %10s\n','Sum','Count');
for i=1:length(count_sum_face_values)
fprintf('%10d %10.4f\n',(i+1),probability_dist(i));
end
% plot the histogram bar chart
bar((2:6),count_sum_face_values);
title('Histogram of the sum face values');
xlabel('Sum');
ylabel('Frequency of occurrence');
%end of script

Output: