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UPSC 2004: 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
(a)3/1000
(b)3/365
(c)1/(365)²
(d)1/(365)³
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Not attemptedCorrect Answer: (c) 1/(365)²
The first student can have any of the 365 possible birthdays. For the other two to match this same day the probabilities are each 1⁄365, so the joint probability is 1 × (1/365) × (1/365)=1/(365)². Hence option (c) is correct; option (d) incorrectly multiplies by an extra 1/365 which would condition on a particular calendar date instead of allowing any day. ([examrobot.com](https://examrobot.com/content/three-students-are-picked-random-school-having-total-1000-students-probability-these-three?utm_source=openai))
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Frequently Asked Questions
What is the correct answer to this UPSC 2004 Science & Technology question?▼
The correct answer is option (c): 1/(365)². Watch the detailed video explanation in our Sherlocking Prelims course on UnlockIAS.
Which year was this Quantitative Aptitude question asked in UPSC Prelims?▼
This question was asked in UPSC CSE Prelims 2004, GS Paper 1, as Question 147. It falls under Science & Technology > Quantitative Aptitude.
What is the difficulty level of this UPSC question?▼
This question is rated "easy". It tests basic recall and most well-prepared aspirants should answer it correctly.
How many UPSC Prelims questions have been asked from Quantitative Aptitude?▼
UPSC has asked 178 questions from Quantitative Aptitude (under Science & Technology) across multiple years. Visit the topic page to see the full list and year-wise trends.