GATE CE 2023 Set 2 — Question 13
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General Aptitude → Quantitative Aptitude → Elementary Statistics & Probability
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Question
A remote village has exactly 1000 vehicles with sequential registration numbers starting from 1000. Out of the total vehicles, 30% are without pollution clearance certificate. Further, even- and odd-numbered vehicles are operated on even- and odd-numbered dates, respectively. If 100 vehicles are chosen at random on an even-numbered date, the number of vehicles expected without pollution clearance certificate is ________.
Correct answer
(B) 30
Solution
1.Total Vehicles: 1000. Registration numbers are 1000, 1001, ..., 1999.
2.Even/Odd Distribution: There are 500 even-numbered vehicles (1000, 1002, ..., 1998) and 500 odd-numbered vehicles (1001, 1003, ..., 1999).
3.Pollution Clearance: 30% of the total vehicles are without certificates. Total without certificates = .
4.Assumption: Assuming a uniform distribution of non-compliant vehicles across even and odd numbers, the number of even-numbered vehicles without certificates is .
5.Expected Value: On an even-numbered date, only even-numbered vehicles are operated. If 100 vehicles are chosen at random from the pool of 500 even-numbered vehicles, the expected number of vehicles without certificates is:
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