Correct Answer: c: 0.16
To find the probability that an arrow falls in the red region, we need to calculate the area of the red region and divide it by the total area of the target.
     Step 1: Calculate the total area of the target.
         ○ The target is a circle with a diameter of 1 m, so its radius is 0.5 m.
         ○ The area of the circle (target) is given by the formula:
       \[ \text{Area}_{\text{total}} = \pi \times (\text{radius})^2 = \pi \times (0.5)^2 = 0.25\pi \, \text{m}^2 \]
     Step 2: Calculate the area of the red region.
         ○ The radius of the red region is 0.20 m.
         ○ The area of the red region is given by the formula:
       \[ \text{Area}_{\text{red}} = \pi \times (\text{radius of red})^2 = \pi \times (0.20)^2 = 0.04\pi \, \text{m}^2 \]
     Step 3: Calculate the probability.
         ○ The probability that an arrow falls in the red region is the ratio of the area of the red region to the total area of the target:
       \[ \text{Probability} = \frac{\text{Area}_{\text{red}}}{\text{Area}_{\text{total}}} = \frac{0.04\pi}{0.25\pi} = \frac{0.04}{0.25} = 0.16 \]
     Therefore, the probability that the arrows fall in the red region of the archery target is 0.16.