Final answer:
The probability of the minter's wrongdoing going undetected is calculated by finding the chance of not selecting the false coin from each box and multiplying these probabilities together since the king draws from 100 boxes.
Step-by-step explanation:
The student is asking about the probability of an event occurring when drawing from a set of items. This falls under the subject of probability theory in mathematics.
The student wants to know the chance that the king's suspicion of the minter's dishonesty goes unchecked after testing coins from each of 100 boxes containing one false coin. To find the probability that the minter's actions go undetected, we would need to calculate the likelihood of not picking the single false coin in each of the 100 boxes.
Since each box has 100 coins and one of them is a false coin, the probability of not picking the false coin from one box is 99/100. Because the king draws from 100 boxes, the probabilities multiply:
P(not picking a false coin in one box) = 99/100
P(not detecting the false coins in 100 boxes) = (99/100)^100
This is the probability of the minter's peculations going undetected, assuming independence of coin draws and only one false coin in each box.