Question

You are given 50 white marbles, 50 black marbles and two jars. You need to put 100 marbles in any of these two jars. The jars will then be shaken and you will be asked to pick one marbles from either jar. How would you distribute the marbles in two are to maximize the possibility of picking a white marble blind folded?

• A. 25 white and 25 black in each.
• B. White in one and 99 in the other.
• C. 50 white in one and 50 black in the other.
• D. All hundred in one.

Answer 1

The Correct Option is B

Scenario	Jar 1	Jar 2	Chance of Picking White
25 white and 25 black in each	25 white, 25 black	25 white, 25 black	50%
White in one and 99 in the other	1 white	99 (49 white, 50 black)	50%
50 white in one and 50 black in the other	50 white	50 black	50%
All hundred in one	100 (50 white, 50 black)	0	50%

To maximize the probability of picking a white marble, strategy 2 is the most effective. In this setup, you put 1 white marble in Jar 1 and the rest (49 white, 50 black) in Jar 2. When you draw from Jar 1, the probability of getting a white marble is 100%. If you draw from Jar 2, the probability is 49/99. Thus, the overall probability of picking a white marble is the average of the probabilities when drawing from each jar. Assume you always choose Jar 1 when available:

Prob(White) = Prob(Choose Jar 1) * Prob(White from Jar 1) + Prob(Choose Jar 2) * Prob(White from Jar 2) = 0.5 * 1 + 0.5 * (49/99) ≈ 0.745, which is 74.5%.

This approach yields the highest possible likelihood of picking a white marble, significantly better than the 50% baseline in other configurations.