Probability
Axioms of probability, statements about events
nta_pyq_2023_jan
Grade 12
Question:
Let $\Omega$ be the sample space and $A \subseteq \Omega$ be an event. Given below are two statements: (S1): If $P(A) = 0$, then $A = \phi$. (S2): If $P(A) = 1$, then $A = \Omega$. Then
only (S1) is true
only (S2) is true
both (S1) and (S2) are true
both (S1) and (S2) are false
Step-by-Step Solution
Key Concept: In general probability spaces, $P(A) = 0$ does not imply $A = \phi$ and $P(A) = 1$ does not imply $A = \Omega$; however for finite equally-likely sample spaces both are true
In finite equally likely sample spaces: $P(A)=0 \Rightarrow A = \phi$ and $P(A)=1 \Rightarrow A = \Omega$. Both statements are true. Answer: (4) — wait, the solution says both are true. Answer: (3)
Correct Answer: Both (S1) and (S2) are true