Let Ω be the sample space and A ⊆ Ω be an event. Given below are two statements: (S1): If P ( A )=0, then A =∅ (S2): If P(A)=1, then A=Ω Then

Question

Let Ω be the sample space and A ⊆ Ω be an event. Given below are two statements: (S1): If P ( A )=0, then A =∅ (S2): If P(A)=1, then A=Ω Then (A) both (S1) and (S2) are true (B) only ( S 1) is true (C) only (S2) is true (D) both (S1) and (S2) are false

Tardigrade Admin · Accepted Answer

Ω= sample space A = be an event If P(A)=0 ⇒ A=φ If P ( A )=1 ⇒ A =Ω Then both statement are true

Q. Let $Ω$ be the sample space and $A \subseteq Ω$ be an event.
Given below are two statements :
(S1): If $P (A) = 0$ , then $A = \emptyset$
(S2): If $P (A) = 1$ , then $A = Ω$ Then

both (S1) and (S2) are true

only ( S 1) is true

only (S2) is true

both (S1) and (S2) are false

$Ω =$ sample space
$A =$ be an event
If $P (A) = 0 \Rightarrow A = ϕ$
If $P (A) = 1 \Rightarrow A = Ω$
Then both statement are true

Q. Let Ω be the sample space and A⊆Ω be an event. Given below are two statements : (S1): If P(A)=0, then A=∅ (S2): If P(A)=1, then A=Ω Then