If you meant this to be a mathematical problem, then you should state the conditions more clearly to present it as a purely mathematical problem. I have heard this problem before, but your description of the problem lends itself to some creative answers because it describes a real world situation. A person choosing a marble randomly in a room from two buckets has too many variables to determine the probability.
Observations:
- You did specify that the new person would choose a marble at random from inside one of the buckets.
- You specified a that a person would choose “randomly” which introduces a lot of variables.
- You did not specify that the choice of bucket was completely random as well as the choice of marble.
Potential solutions that exploit the above observations:
1)Put all of the marbles in one bucket. Put the other bucket on top of of the full one upside-down. Put a single blue marble inside the rim of the bottom of the upside-down bucket. A bucket has two concave surfaces, either of which can be considered “inside” under normal assumptions. Under topographical assumptions, neither could be considered “inside” the bucket.
- Melt the plastic of both buckets. Put the white marbles into this goo and reform the plastic into a new bucket made of plastic and white marbles. Place the blue marbles into this new bucket. Both the white and blue marbles are inside of both buckets.
- Leave a post-it note: “Take One” on the blue marble bucket.
- Completely fill one bucket until it is brimming with all of the white marbles and pee. Leave the blue marble bucket as is.
- Put all of the white marbles in one bucket, then the second bucket with blue marbles on inside of that bucket covering the white marbles.
- Cover the white marble bucket with your shirt and turn it upside-down. Slide your shirt away to leave the white marbles contained by the upside-down bucket. Then place the full blue bucket on top of the upturned white bucket.
- Stack the buckets so you can climb to the ceiling. Hide the white marbles bucket in the ceiling.