ExamHabit
Practise free

JEE Main 2023 · 24 Jan · Shift 1 · Paper-1(B.E./B. Tech.)

JEE Main 2023 Mathematics question on Probability

Let Ω\Omega be the sample space and A⊆ΩA \subseteq \Omega be an event.

Given below are two statements :

(S1) : If P(A)=0P(A) = 0, then A=∅A = \emptyset

(S2) : If P(A)=1P(A) = 1, then A=ΩA = \Omega

Then
  1. A.
    both (S1) and (S2) are false
  2. B.
    only (S1) is true
  3. C.
    both (S1) and (S2) are true
  4. D.
    only (S2) is true
Show answer and solution

Correct option: C

Solution

Both statements are false in general probability theory (e.g., on continuous sample spaces, a single point has probability 0 but is not the empty set). However, in the JEE context, the sample space Ω is taken to be a finite set with equally likely outcomes (classical probability). In this setting, P(A) = 0 means the number of favorable outcomes is 0, so A must be ∅, and P(A) = 1 means all outcomes are in A, so A = Ω. Under this classical/finite interpretation, both S1 and S2 are true.

[JEE Main 2023 · 24 Jan · Shift 1 · Paper-1(B.E./B. Tech.)]

Practise Probability the way it is asked

A timed set of real JEE Main Probability questions, graded as the exam grades. No sign-up.

Start a Probability test

More: all JEE Main Probability questions · JEE Main 2023 · Mathematics chapter list