Choosing balls from the boxes

I found the following question to solve: Game with 13 boxes(no repetitions). Inside each box there is a ball of different colour. There are 3 colours (red, blue and green), and there are 4 balls per colour. One box contains a black ball.

Win: when we pick 4 of the same colour - award: red - 10, blue - 20, green - 50

Loose: when we find black - no award

I would like to write a program, to find the probability of picking the black ball before any 4 of the same colour was found.

My first idea was to write a "for" and than many "if" statements but my plan didn't work:

rCount: # of red balls founded

n = 13

for i = 1:n

if rCount == 4

disp('You won the game with red')

else \\'I would like to write here a code like keep going with the loop'

end

[Torsten]

I would like to write a code solving this problem.

You didn't state what the problem is.

[Sam Chak]

@Michal Waligora

Did you get stuck after end?

[Michal Waligora]

True, Question: write a program, to find the probability of picking the black ball before any 4 of the same colour was found

Answer 1

[Torsten]

  positions_red = 1:4;
  positions_blue = 5:8;
  positions_green = 9:12;
  position_black = 13;
  
  Ntrials = 1e5;
  success = 0;
  for i = 1:Ntrials
    draw = randperm(13);
    draw_black = find(draw==position_black);
    draw = draw(1:draw_black-1);
    redindraw = numel(intersect(draw,positions_red));
    blueindraw = numel(intersect(draw,positions_blue));
    greenindraw = numel(intersect(draw,positions_green));
    if redindraw < 4 && blueindraw < 4 && greenindraw < 4
      success = success + 1;
    end
    if mod(i,1000)==0
      disp(i)
    end
  end
  probability = success/Ntrials

[Michal Waligora]

Wow, that's great. Thank you