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
 

• A. 15
• B. 30
• C. 50
• D. 70

Hint:

When choosing a random sample of vehicles, divide the total number by the sample size and multiply by the proportion of the group (in this case, the vehicles without the certificate).

Answer 1

The Correct Option is B

Given that there are 1000 vehicles in total and 30% of them do not have a pollution clearance certificate, we can calculate the number of vehicles without the certificate as:
\[ 30% \text{ of } 1000 = 0.30 \times 1000 = 300 \text{ vehicles without pollution clearance certificate}. \] Since the vehicles are operated on even-numbered dates and we are choosing 100 vehicles at random on an even-numbered date, we expect 50 of the selected vehicles to be even-numbered and 50 to be odd-numbered.
Thus, the number of vehicles without a pollution clearance certificate expected on an even-numbered date would be:
\[ \frac{50}{1000} \times 300 = 30 \text{ vehicles without pollution clearance certificate.} \] So, the correct answer is (B).