Question

which probability would be least likely when throwing one dart, assuming that the dart will land on the board?

Explanation:

Step1: Recall probability formula

The probability \( P \) of an event is given by \( P=\frac{\text{Area of the region}}{\text{Total area of the dartboard}} \).

Step2: Analyze the areas

The 20 - point region is the innermost circle, so its area is the smallest among the regions (5, 10, 15, 20 - point regions). The total area of the dartboard is fixed.

Step3: Relate area to probability

Since the probability is proportional to the area of the region (when the dart lands randomly on the board), the smaller the area of a region, the smaller the probability of the dart landing on it. As the 20 - point region has the smallest area among the given regions, the probability of landing on the 20 - point region is the least likely.

Answer:

The probability of landing on the 20 - point region.