2004 General Studies, all questions
UPSC Prelims 2004 · General Studies
Question 147: Basic Numeracy
Three students are picked at random from a school having a total of 1000 students. The probability that these three students will have identical date and month of their birth is
a3/1000
b3/365
c1/(365)²
d1/(365)³
AnswerThe answer is (c).
The first student can have any birthday. The second must match it, with probability 1/365, and the third must match it too, another 1/365. So the probability is (1/365) x (1/365) = 1/(365)². The size of the school does not matter, and birthdays are taken as equally likely over 365 days.
Why each option is right or wrong
- (a) 3/1000 confuses the sample with the birthdays.
- (b) 3/365 adds the matches instead of multiplying them.
- (c) Correct: 1/365 for each of the two matches gives 1/(365)².
- (d) 1/(365)³ would be the chance that all three match a date fixed beforehand.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2004, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.