You have two bags, 50 red balls and 50 blue balls. How will you arrange the balls in two bags such that probability of picking up red ball is maximum?

There are different ways to keep the balls. If you mix the balls equally then probability would be same for both the balls from both the bags. If you keep different balls in different bag then also probability becomes 50-50 as one bag has 100% chances whereas another has 0% chance.

So in order to increase the probability of picking up red ball, put only one red ball in one bag and rest of the red and blue ball in another bag. So here the probability of picking up a red ball becomes 100% for one bag and approximately 49% for second bag. So the 100%-49% probability is better than other solution of 50%-50% and 100%-0%.

Let me know if you have more optimize solution.

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Interesting to know.

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