>>16791006
Here's an experiment you could run first. Put together a sample of a few hundred people and blindfold them. Take two dice, one that has 6s on all its faces and one that has 1s on all its faces. Have them pick a die and tell them they have to roll twice with the same die. Clean the data afterward to only include people who rolled a 6 on the first roll. Show us the experimental probability of rolling a 6 again on the second roll.

But running this would be a tremendous waste of time, because you can easily calculate the probability. Well, you can use virtually the same math to calculate the probability of drawing a gold ball in your own scenario.