A round archery target of diameter 1 m is marked with four scoring regions from the centre outwards as red, blue, yellow and white. The radius of the red band is 0.20 m. The width of all the remaining bands is equal. If archers throw arrows towards the target, what is the probability that the arrows fall in the red region of the archery target?

Correct Option: (c) 0.16

The target is circular with a diameter of 1 m, which means its total radius R = 1 / 2 = 0.50 m. The total area of the target is given by Area_total = pi × R^2 = pi × (0.50)^2 = 0.25 × pi square meters. The target is divided into four regions: red, blue, yellow, and white from the center outwards. The red region is the innermost circle with a radius of r = 0.20 m. The area of this red region is Area_red = pi × r^2 = pi × (0.20)^2 = 0.04 × pi square meters. 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. Thus, Probability = Area_red / Area_total = (0.04 × pi) / (0.25 × pi) = 0.04 / 0.25 = 4 / 25 = 0.16. Therefore, the probability is 0.16, making option (c) the correct choice.