The Blue Gems
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There are hundred red gems and hundred blue gems. The blue gems are priceless while the red gems equal wastage. You have two sacks one labeled Heads and the other Tails. You have to distribute the gems as you want in the two sacks. Then a coin will be flipped and you will be asked to pick up a gem randomly from the corresponding sacks.
How will you distribute the gems between the sacks so that the odds of picking a Blue gem are maximum? 
I will put one blue gem in one sack and the other 99 gems into the sack with the red gems so now the probability will we 0.5 * (1/1 + 99/199) = 0.7487 which is almost 3/4
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