Correct Option (3)
The total area of the archery target is calculated using its diameter. Given the diameter is 1 m, the radius (R) is 0.5 m.
- Total Area = πR2 = π(0.5)2 = 0.25π m2.
The radius of the red band (rred) is given as 0.20 m.
- Area of Red Band = π(rred)2 = π(0.20)2 = 0.04π m2.
The probability that an arrow falls in the red region is the ratio of the area of the red band to the total area of the target.
- Probability = (Area of Red Band) / (Total Area) = (0.04π) / (0.25π) = 0.04 / 0.25 = 4/25 = 0.16.
Incorrect Options:
- Option 1 (0.40): This value does not represent the probability. It might be derived from a miscalculation, such as considering twice the radius of the red band (2 * 0.20 = 0.40) or a misinterpretation of area ratios.
- Option 2 (0.20): This value corresponds to the radius of the red band, not the probability of an arrow falling within it. Probability is a dimensionless ratio of areas.
- Option 4 (0.04): This value represents the square of the radius of the red band (0.202) or the area of the red band divided by π (0.04π / π). It is not the probability, which requires a ratio of the red band's area to the total target area.
