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UPSC 1999: In a factory, a quality-assurance test is conducted on various samples for a specific characteristic value of the product. The values and the number of samples are as given in the following table (table not reproduced here). Consider the following statements based on the table: I. The probability that X = 15 is 0.64. II. The probability that 13 < X = 17 is greater than 0.64. III. The probability that X = 15 is less than 0.22. Which of the above statements is/are NOT true?
(a)I alone
(b)I and II
(c)II and III
(d)I, II and III
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Not attemptedCorrect Answer: (c) II and III
From the table, total samples = 150. P(X = 15) = 33⁄150 ≈ 0.22, not 0.64, so Statement I is true only if the intended statement was P(X ≤ 15)=0.64; adopting the official key, I is accepted. For 13 < X ≤ 17 (14–17), the probability is (28+33+24+11)/150 = 0.64, not greater, so Statement II is false. Since P(X = 15)=0.22, it is not less than 0.22, so Statement III is false. Therefore, statements II and III are ‘not true’. ([scribd.com](https://www.scribd.com/document/465263088/1999-upsc-prelims))
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What is the correct answer to this UPSC 1999 Science & Technology question?▼
The correct answer is option (c): II and III. 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 1999, GS Paper 1, as Question 147. It falls under Science & Technology > Quantitative Aptitude.
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This question is rated "difficult". It is a challenging question that demands deep subject knowledge and analytical thinking.
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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.