You need to place all the marbles into the jars?

Question

You have two jars, 50 red marbles and 50 blue marbles. You need to place all the marbles into the jars such that when you blindly pick one marble out of one jar, you maximize the chances that it will be red. When picking, you’ll first randomly pick a jar, and then randomly pick a marble out of that jar. You can arrange the marbles however you like, but each marble must be in a jar.

Answer 1

In one jar you put only 1 red marble.
All the other marbles (49 red + 50 blue) go in the other jar.
Your changes of picking a red marble is:
50% of picking the jar with 1 marble * 100% of picking a red marble from that jar = 50%
50% of picking the jar with 99 marbles * 49/99% of picking a red marble from that jar = 49.5%
Change of picking a red marble = 50 + 49.5 = 99.5%