Answer:
There should be at most 24 lucky numbers in the third bag.
Step-by-step explanation:
Initially, there are 200 numbers. Two bags with 100 each. There are 31+18 = 49 lucky numbers. So there is a 49/200 = 0.245 probability that a randomly selected number from a random bag is the lucky number.
Now with 300 numbers, we want this probability to be lower than 24.5%. So we should solve the following rule of three:
200 - 49
300 - x
With the third bag, the probability will be the same if 73.5-49 = 24.5 lucky numbers are added. So there should be at most 24 lucky numbers in the third bag.