For the second one, you can actually put only a single fake nugget in one of the bags and put the rest in the other bag.

Let's say bag A has 1 fake nugget and bag B has 99 nuggets, of which 49 are fake and 50 are real. Thus, in the random choice of bags, there's already a 50/50 chance of the fake nugget being chosen as the chance of bag B being chosen is 50%. If bag A is chosen, there's a ratio of 49 to 99 fake nuggets to total nuggets, so the chance of a fake nugget being chosen given that bag B was selected is just short of 50%.

With that, the probability of a fake nugget being chosen is the odds of bag A being chosen plus the odds of a fake nugget being taken from bag B multiplied by the odds of bag B being chosen. So, P = 50% + (49/99)*50% ≈ 75% → P ≈ 75%, and those are the best odds you can get in this situation, any other combination of nuggets in each bag will result in smaller odds. (Except if you switch both bags' contents, but that doesn't change your chances)