On the outermost layer of the rings (where the electrons are)
To determine whether the crown was made of pure gold or not, we need to compare the density of gold (19.3 g/mL) to the density of the crown.
The formula for density is

we know the mass of the crown is 714 grams and its volume is 38.3 mL. (Because it displaces 38.3 mL of water)
Using this information, we can plug the numbers into our density formula to solve for the density of the crown.

The density of the crown is 18.6 g/mL, thus the crown was not made of pure gold, as that has a density of 19.3 g/mL. In conclusion, the goldsmith tried to screw over the king.
Given that the drum is replaced each time before sampling, the selections are independent events. Then, the probability of the combined event is the product of each probability: (50/5000) * (50/5000) * (50/5000) = (1/100)^3 = 0.000001