On a square target, the probability of a dart hitting the shaded square, which is half the area of the target, is 1/2 and the correct option is A.
The probability of an event happening is defined as the ratio of the number of outcomes that favor the event to the total number of possible outcomes. In this case, the event we are interested in is the dart hitting the shaded square. The total number of possible outcomes is the number of ways that the dart can land on the target. Since the dart can land on any spot on the target with equal likelihood, there are infinitely many possible outcomes.
To count the number of outcomes that favor the event, we need to count the number of ways that the dart can land in the shaded square. Since the shaded square is perfectly centered in the target, there are just as many ways for the dart to land in the shaded square as there are ways for it to land in the rest of the target. Therefore, the number of outcomes that favor the event is also infinitely many.
Since both the number of outcomes that favor the event and the total number of possible outcomes are infinitely many, the probability of the event happening is also infinitely many. However, we can still say that the probability of the dart hitting the shaded square is 1 / 2. This is because the ratio of the number of outcomes that favor the event to the total number of possible outcomes is 1 / 2.
Therefore, the correct option is A.