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 target's radius is 0.5 m and the red band's radius is 0.20 m.
• Probability = red area ÷ total area = (π × 0.20 × 0.20) ÷ (π × 0.5 × 0.5) = 0.04 ÷ 0.25.
• 0.04 ÷ 0.25 = 0.16.
• Hence 0.16, option (c).
Why the other options are wrong
- (a) 0.40
- 0.40 is the ratio of radii (0.20 ÷ 0.5), not of areas.
- (b) 0.20
- 0.20 is the red radius, not a probability.
- (d) 0.04
- 0.04 is the red area divided by π, not the ratio of areas.
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.