This is a really tricky probability problem. I have had many 'arguments' over the fact that the probability of drawing a white counter IS NOT 1/2! Set the Number of Trails slider to a value from 100 to 1000. Click on the green flag. The number of times a white counter was drawn and the number of times a black counter was drawn is accumulated and displayed. Running this project at high 'Number of Trials levels' should help you form an intuitive conjecture of the value of the theoretical probability.
Tried to get the algorithm closer to the actual process.