Let's say I have a set of items out of which I randomly take 5% . Then perform some action on these items and put them back in the set.
After how many repetitions of this process can I be 95% sure that I have performed this action on all the items.

For illustrative purposes -- Let's say I take 5 ping-pong balls blindly out from a sack where there are originally 100 white balls. I paint/repaint those I have taken red and put them back in the sack. After how many tries can I be 95% sure that all the balls in sack are now red.
What would the general form for the calculation be for other sample sizes and probabilities. (10% of balls and 75% chance etc.)