Let Ω be the sample space and A ⊆ Ω be an event. Given below are two statements: (S1): If P…

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

(S1): If P(A)=0, then A=ϕ

(S2): If P(A)=, then A=Ω

Then

  1. only (S1) is true
  2. only (S2) is true
  3. both (S1) and (S2) are true
  4. both (S1) and (S2) are false

Solution

Given:

Ω=sample space

A=be an event

So, 

If P(A)=0⇒A=ϕ

If P(A)=1⇒A=Ω

Hence, both statements are true.

Asked in: JEE Main 2023 (24 Jan Shift 1)

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