How to make a properablity eqautions

Hello MathWorks,

I want to make a program that calculates properablity or chances of selected numbers. However I also want to make a program that show the selected numbers. For explain you know how fliping a coin is 50/50 but when you flip its either head or tails. I would like to make a program where I can have a setting or range of numbers between for ex 1 to 10 and the program run 3 numbers between that range and tell me its probability. I know its simple i just dont know how to do it. Thank you

Answer 1

[BhaTTa]

Hey @Rainaire Hansford, I have attached simple MATLAB script that will:

1. Let you specify a range of integers (e.g. 1 to 10).
2. Randomly draw N numbers from that range (with or without replacement).
3. Display each draw.
4. Repeat the experiment M times to estimate the probability of each possible number appearing in the draw.

below i have attached the code, please take it as reference and modify it accordingly:

%% SETTINGS
minVal    = 1;      % Minimum in range
maxVal    = 10;     % Maximum in range
Ndraw     = 3;      % How many numbers drawn each trial
withRepl  = false;  % true = allow repeats, false = no repeats
Mtrials   = 10000;  % How many experiments to run

%% PREPARE
values    = minVal:maxVal;
K         = numel(values);
countHits = zeros(1,K);    % count of times each value was drawn
allDraws  = zeros(Mtrials,Ndraw);  % record of every draw

%% RUN EXPERIMENTS
for t = 1:Mtrials
    if withRepl
        % Draw Ndraw samples with replacement
        draw = values(randi(K,1,Ndraw));
    else
        % Draw Ndraw samples without replacement
        draw = values(randperm(K,Ndraw));
    end
    allDraws(t,:) = draw;
    
    % Count each drawn value
    for v = draw
        idx = v - minVal + 1;  % index into countHits
        countHits(idx) = countHits(idx) + 1;
    end
end

%% DISPLAY ONE EXAMPLE
exampleRun = 1;  % Change to any trial index 1..Mtrials
fprintf('Example draw #%d: ', exampleRun);

Example draw #1: 

fprintf('%d ', allDraws(exampleRun,:));

10 9 8 

fprintf('\n\n');

%% ESTIMATE PROBABILITIES
% Each trial draws Ndraw numbers, so total draws = Mtrials*Ndraw
totalDraws = Mtrials * Ndraw;
probEst    = countHits / totalDraws;

% Show results in a table
T = table(values.', countHits.', probEst.', ...
    'VariableNames',{'Value','Count','EstimatedProbability'});
disp(T);

    Value    Count    EstimatedProbability
    _____    _____    ____________________

      1      3073            0.10243      
      2      2984           0.099467      
      3      2989           0.099633      
      4      2927           0.097567      
      5      3035            0.10117      
      6      3049            0.10163      
      7      2993           0.099767      
      8      3052            0.10173      
      9      2936           0.097867      
     10      2962           0.098733      

%% PLOT THE DISTRIBUTION
figure;
bar(values, probEst);
xlabel('Value drawn');
ylabel('Estimated Probability');
title(sprintf('Estimated Probability of Drawing Each Value (%d trials × %d draws)', Mtrials, Ndraw));
grid on;