In a box there are 4 identical indistinguishable balls numbered from 0 to 3. Remove them at random successively and without exchanging two balls from the bag. Let Z be the queried variable "product of said numbers". For a certain value of K, we have that: P(Z = K) = 1/2. What is the value of K?

Solution: The set of possible pairs of numbers, along with their products Z in parentheses, are the following: 0, 1 (0) 0, 2 (0) 0, 3 (0) 1, 2 (2) 1, 3 (3) 2, 3 (6) The probability of Z=K happening is 1/2. Therefore, K comes out 50% of the time. In the 6 possible combinations, three should be the same, and the only value that satisfies this probability is zero, which comes out 3 out of 6 combinations. Therefore, K=0. Answer: K=0