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If A and B are two events such that P(A) $\neq$ 0 and P(B | A) = 1 . Then choose the correct answer.

\[ \begin{array} (A)\: A \subset B \quad & (B)\: B \subset A \quad & (C)\: B = Ø \quad & (D) \: A = \phi \end{array} \]

1 Answer

Given $P(A) \neq 0 \: \text{and}\: P(B | A) = 1$
$\rightarrow P \large (\frac{B}{A}) = \frac{P (A \cap B)}{P(A)} $$= 1$
Therefore, $P (A \cap B) = P (A)$, which means $A \cap B = A \rightarrow A \subset B$
answered Jun 22, 2013 by balaji.thirumalai
 

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