2006 General Studies, all questions
UPSC Prelims 2006 · General Studies
Question 68: Basic Numeracy
3 digits are chosen at random from 1, 2, 3, 4, 5, 6, 7, 8 and 9 without repeating any digit. What is the probability that their product is odd?
a2/3
b5/108
c5/42
d7/48
AnswerThe answer is (c).
A product of three numbers is odd only if all three are odd. Among 1 to 9 there are 5 odd digits (1, 3, 5, 7, 9). Favourable choices: C(5,3) = 10. All choices of 3 digits from 9: C(9,3) = 84. Probability = 10/84 = 5/42.
Why each option is right or wrong
- (a) 2/3 is far too high; only 5 of the 9 digits are odd.
- (b) 5/108 does not match 10 favourable out of 84.
- (c) Correct: 10/84 = 5/42.
- (d) 7/48 does not match 10 favourable out of 84.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2006, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.