You have two jars, 50 red marbles and 50 blue marbles. A jar will be picked at random, and then a marble will be picked from the jar. Placing all of the marbles in the jars, how can you maximize the chances of a red marble being picked? What are the exact odds of getting a red marble using your scheme?
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Place all the marbles except one of type X into a single jar, then place the marble of type X in the other jar. Then the odds of drawing a marble of type X when reaching into the jar that only contains a single marble of type X are 100%. The odds of drawing a marble of type X when drawing from the other Jar are 49 out of 99 or ((49/99)*100)%. When choosing from both jars the odds of drawing a marble of type X are (100% + ((49/99)*100)% /2).