You have succeeded in going to the top of a brainvita (a contest with prizes). Your final task lays ahead of you.
There are 100 table tennis balls and 2 empty bowls in front of you. Out of the 100 balls, 50 are white and 50 are yellow in color. Now, you are asked to fill the bowls in any manner you like (using all the balls).
After you are done, you will be blindfolded and the bowls will be shuffled. Then, you will be asked to pick up a ball from any bowl. If the ball you pick up is yellow, you will win the grand prize and if you pick up the white ball, you will not win anything.
How will you increase your chances of winning?
Solution:
The best way to increase the probability of winning is to place one yellow ball in the first bowl and all the other balls in the second bowl.
Now, you have a 1/2 probability of choosing the bowl with just one yellow ball. If you choose that, you win.
If you choose the other bowl, it has 49 yellow balls and 50 white balls. You still have almost 1/2 probability of picking a yellow ball out of it and winning.