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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 ________.

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GATE CE 2023 Official Paper: Shift 2
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  1. 15
  2. 30
  3. 50
  4. 70

Answer (Detailed Solution Below)

Option 2 : 30
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Solution:

Probability of selecting even vehicles on even numbered dates = 1

Since 30% of the total vehicles are without pollution clearance certificate.

∴ The no. of vehicles expected without pollution clearance certificate

= 100 × 1 × 0.3

= 30

30 vehicle are expected to be without pollution clearance certificate.

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