Explanation

In this question, we need either to get the value of a probability or at least determine whether the probability is definitely less than one-half or definitely equal to or greater than one-half. We can potentially get this information directly about white and green probabilities or from the negative case of the other colors. On to the data statements! Separately first, of course.

Statement (1) gives us the probability of a gray ball. Namely, 4 of the 12 balls are gray. We don't know how many black balls there are. If there is 1 black ball, then there are 7 white or green balls and the probability of white or green is greater than one half. But another admissible case is that there are 6 black balls, and in that case there would be only 2 white or green balls, and the probability would be less than one half. Different answers are possible in different cases, so we have insufficient data to answer the question.

Statement (2) is insufficient by the same logic--we can construct a case with a large number of white balls or a small number. Insufficient.

Putting the statements together, we now know the colors of 6 of the 12 balls. There are still enough undetermined colors to come up with both cases: for example, 5 white and 1 black, or 5 black and 1 white. Insufficient.

The correct answer is (E).