This one was a relatively simple puzzle, though not really for children below 12 years as they are not as familiar with the probability concept. I am not posting a video solution to this as there is not much value in a video solution for this one.
The way to maximize the probability of getting a red ball is to put just one red ball into one of the containers and all the other 99 balls (49 reds and 50 whites) in the other container. The probability of getting a red ball is as follows:
(1/2)*1 + (1/2)*49/99 = ~0.75
I do not have any proof that this it the best way to do it. But if anyone has a proof, I would love to see it and post it for other people’s benefit.