UPSC Prelims 2016 · CSAT
Question 79: Basic Numeracy
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 ?
AnswerUPSC’s answer is (c).
A diameter of 1 m means a radius of 0.5 m. The probability equals the red area over the total area: (0.2)^2 / (0.5)^2 = 0.04 / 0.25 = 0.16. Pi cancels, and the widths of the other bands do not matter. Remember: for an arrow landing at random, probability = favourable area / total area, and areas go with the square of the radius.
Why each option is right or wrong
- (a) 0.40 is the ratio of radii, not of areas.
- (b) 0.20 is the red radius in metres.
- (c) Right: 0.04 / 0.25 = 0.16.
- (d) 0.04 is the red area before dividing by the total.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2016, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.