PUZZLE OF THE DAY

QUESTION:-
Once Birbal was returning from a visit to a far land when his ship capsized. He was taken prisoner by a mad king in a distant land who had heard of Birbal's intelligence. The king wanted to see how intelligent Birbal really was. He gave Birbal two large jars - one with 50 red marbles and the other with 50 white marbles. He allowed Birbal to move the marbles around between two jars. The only condition was that each of the 100 marbles should finally be accounted for in one of the two jars.

After Birbal finished, he would be blindfolded and the two jars will be shaken. Then the king will chose one of the jars at random and give that jar to Birbal. Birbal will have to pick one marble out of that jar. If he picks a white marble, he will be set free and sent home in comfort; if he picks a red marble, he will be given 100 lashes and sent-off on a boat without food or water.

What should Birbal do to maximize his chances of picking a white marble?

 Solution


Birbal leaves one white marble in the first jar and transfers the rest to the second jar. The probability of drawing a white marble from the first jar is 1 (100%). The probability of drawing a white marble from the second jar is 49/99.
Given that either of the two jars is equally likely to be picked up, the combined probability is (0.5 x 1) + (0.5 x 49/99) = 74/99. That's a 74.75% chance of drawing a white marble.