Question

you have 10 black marbles, 10 white marbles, and 2 buckets. i am going to pick one of the two buckets at random and select one marble from it at random. how would you fill the two buckets with marbles to maximize the odds that i select a white marble?

Answer 1

To maximize the odds of selecting a white marble, you can fill one bucket with all the white marbles and the other bucket with all the black marbles.

Answer 2

To maximize the chances of selecting a white marble, place one white marble in one bucket and the remaining white and black marbles in the second bucket. This setup ensures a 100% chance from the first bucket, and a 9/19 chance from the second.

Step-by-step explanation:

To maximize the odds of selecting a white marble, you would want to distribute the marbles in such a way that it increases the probability of picking a white marble regardless of which bucket is chosen. The best distribution would be to put one white marble in one bucket and the remaining 19 marbles, which include 9 white and 10 black, in the other bucket.

If you pick the first bucket, you are guaranteed to pick a white marble, as it's the only marble there. The probability is 100% or 1. If you pick the second bucket, the probability of picking a white marble is 9/19. This situation offers much better overall odds than an even spread of marbles.

Therefore, this setup maximizes the probability of selecting a white marble because it gives you the highest possible chance of picking a white marble from either bucket.