Three Buckets Have Marbles

Record how many whites and how many blacks you have.

Three buckets have marbles.

You can justify if you write the probability equations. In this game of chance you select a bucket and then select a marble from within that. Find the probability that the marble is. B from bucket 3 given the marble is white.

Assume buckets have large size. You are allowed to double the number of marbles in a bucket by borrowing from one of the other two buckets. You can move water from one bucket to another only if the bucket to which water is being transferred doubles the amount of water it has. If the marble you pulled out is black put two black marbles back in.

You are allowed to double the number of marbles in a bucket by borrowing from one of the other two buckets. You have the probability p1 for one bucket to take in the first attempt a white marble the same for a probability p2. Seriously though i think several key pieces of info are missing. X y z are integers.

1 after re arrangement do you only get one opportunity to pull a marble fro. In other words you get to take 2 measurements or comparisons here. 3 you are allowed to use set the scale twice in total. Prove that it is possible to produce an empty bucket with a series of such operations.

Three buckets have marbles. We assume marbles are equally to be taken and the total amount is the same in the two buckets where the total is 2m where m is the number of total white marbles and the same quantity for black marbles and m is too the. So all moves have to of the form. If you pulled out a white marble put two white marbles back in.

Bucket 1 has 4 red and 1 white marbles bucket 2 has 6 red and 4 white marbles and bucket 3 has 3 red and 5 white marbles. Then put at least one blue marble in the now empty bucket. Given 3 buckets containing x y z litres of water. 4 each bucket has enough room for multiple marbles.

As long as you have the same number of marbles in each side the heavy marble has just enough weight to tip the scale to its side. A from bucket 3 and the marble is white. Now there are three marbles in the bucket. What i am looking for is the probability that i should assign to each of the three marbles so that i get to.

I have three buckets with marbles. Prove that it is possible to produce an empty bucket with a series of such operations. Three buckets have marbles. Bucket 1 has 2 red marbles and 1 blue marble bucket 2 has 1 red and 1 blue marble and bucket 3 has 3 red marbles and 1 blue marble.