Let be the sample space and be an event. Given below are two statements (S1) : If P(A) = 0, then A = (S2) : If P(A) = 1, then A = Then [2023]

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Solution

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 = $ϕ$

(S2) : If P(A) = 1, then A = $Ω$

Then [2023]

1 both (S1) and (S2) are true

2 only (S1) is true

3 only (S2) is true

4 both (S1) and (S2) are false

Ans.
(1)

$Ω$ be the sample space and A be an event. If $P (A) = 0 \Rightarrow A = ϕ$ If $P (A) = 1 \Rightarrow A = Ω$

Then both statements are true.

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