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NDA 2023 Maths · Mathematics · Probability · medium

If P(A)=0, then A is necessarily the empty set. 2. The mean of a data set is always equal to one of its observations.

Single correct option

Consider the following statements:
1. If P(A)=0P(A)=0, then AA is necessarily the empty set.
2. The mean of a data set is always equal to one of its observations.
Which of the statements given above is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (D) Neither 1 nor 2

An event of probability zero need not be empty: choosing a point at random on a line segment gives probability zero for each single point; so Statement 1 is false. The mean of 1,21,2 is 1.51.5, which is not an observation, so Statement 2 is false too.
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Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake