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NDA 2019 Maths · Mathematics · Probability · easy

For any event A, P(A)+P(bar A)=1. 2. If A⊂ B, then P(A)≥ P(B).

Single correct option

Consider the following statements:
1. For any event AA, P(A)+P(Aˉ)=1P(A)+P(\bar A)=1.
2. If A⊂BA\subset B, then P(A)≥P(B)P(A)\ge P(B).
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: (A) 1 only

Statement 1 holds because an event and its complement are exclusive and exhaustive. For statement 2: if A⊂BA\subset B, every outcome in AA is in BB, so P(A)≤P(B)P(A)\le P(B), the reverse of what is stated; hence it is false. Only statement 1 is correct.
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Original question written in the NDA 2019 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