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JEE Main 202324 JanuaryMorning Shift
Exam
JEE Main
Year
2023
Date
24 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Probability

JEE Main 2023 · 24 January · Morning Shift · Mathematics · Probability

Let Ω be the sample space and A ⊆ Ω be an event. Given below are...

Let ΩΩ be the sample space and A⊆ΩA ⊆ Ω be an event. Given below are two statements:

(S1): If P(A)=0P ( A ) = 0, then A=ϕA = ϕ

(S2): If P(A)=P ( A ) =, then A=ΩA = Ω

Then

Options

  1. Aonly (S1) is true
  2. Bonly (S2) is true
  3. Cboth (S1) and (S2) are true
  4. Dboth (S1) and (S2) are false

Correct answer

C. both (S1) and (S2) are true

Step-by-step solution

Given:

Ω=Ω =sample space

A=A =be an event

So,

If P(A)=0⇒A=ϕP ( A ) = 0 ⇒ A = ϕ

If P(A)=1⇒A=ΩP ( A ) = 1 ⇒ A = Ω

Hence, both statements are true.

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