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 ?

(a) 0.40
(b) 0.20
(c) 0.16 ✓ UPSC's answer
(d) 0.04

Why the answer is (c)

['- The total diameter of the target is 1 m, so the total radius is 0.5 m.', '- The red region is a central circle with a radius of 0.20 m.', '- The area of the red region is calculated as $\\pi \\times (0.20)^2 = 0.04\\pi$ square meters.', '- The total area of the target is calculated as $\\pi \\times (0.5)^2 = 0.25\\pi$ square meters.', '- The probability is the ratio of the red area to the total area: $0.04\\pi / 0.25\\pi = 0.04 / 0.25 = 0.16$.', '- Therefore, the correct probability is 0.16, which corresponds to option (c).']

Why the other options are wrong

(a) 0.40: 0.40 is incorrect because it likely results from comparing the red radius (0.20) to the total diameter (1.0) or making a calculation error in the area ratio.
(b) 0.20: 0.20 is incorrect because it is simply the radius of the red region, not the probability derived from the area ratio.
(d) 0.04: 0.04 is incorrect because it represents the coefficient of the red area ($0.04\pi$) without dividing by the total area coefficient ($0.25\pi$).

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.