The main question has been ably dealt with by (at this time) Jonathan Rich and FAS.
OP, in the comments, brought up the question of strategy in a multiple choice test, if one is essentially out of time and has to guess. For concreteness let us assume there are $30$ questions, with $3$ choices on each question, a), b), and c), only $1$ of which is correct.
Imagine that the teacher made sure that a) was always the correct answer, and then used a good randomizing device to scramble the labels of each choice. Then we are back at the "rare item" question of the OP, and conclude that there is no strategy available to the student.
But possibly the teacher wanted all correct answers to appear exactly $10$ times.
Then if we guess a) each time, we will get exactly $10$ right.
If we randomize our guesses, using a fair die each time to make the decision, then on any question our probability of being right is $1/3$. It turns out that the mean number of correct answers will be $10$, precisely the same as if we guess a) each time. But the variance will be much greater. If the passing mark is $15$, then ticking a) each time leads to a sure fail. A randomized strategy, by contrast, gives a reasonable shot at passing, at the cost of a significant probability of getting a very low mark.
People making up tests get nervous about having consecutive correct choices be the same. Perhaps one could exploit that nervousness and devise improved guessing strategies. One would need data.