Balls and Bowls Puzzles

How should 50 red and 50 blue balls be distributed between two bowls so as to maximize the chance of picking a red marble?

Solution:

Put 1 red marble in bowls A and put the remaining 99 marbles in bowls B. There’s a 50% chance of selecting the bowls containing 1 ball with a 100% chance of selecting a black ball from that bucket. And a 50% chance of selecting the bowls containing 99 balls with a ~49.5% (49/99) chance of selecting a black ball from that bowls. Total probability of selecting a black ball is (50% % 100%) + (50% * 49.5%) = 74.7%