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 (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 (r_red) is given as 0.20 m.

• Area of Red Band = π(r_red)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.