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# A and B are two events such that P (A) $\neq$ 0. Find P(B|A), if (i) A is a subset of B (ii) A $\cap$ B = $\phi$

$\begin{array}{1 1}(i) 1 \quad (ii) 0 \\ (i) 0 \quad (ii) 1 \\ (i) 1 \quad (ii) 1 \\(i) 0 \quad (ii) 0 \end{array}$

Toolbox:
• If A is a subset of B, (A $\subset$ B), then P (A $\cap$ B) = P (A)
• $P \large(\frac{B}{A}) =$$\large (\frac{P(A\;\cap\; B)}{P(A)}) (i) If A is a subset of B, (A \subset B), \rightarrow P (A \cap B) = P (A) Therefore, P \large(\frac{B}{A}) =$$ \large (\frac{P(A\;\cap\; B)}{P(A)}) = \frac{P(A)}{P(A)} $$= 1 (ii) A \cap B = \phi \rightarrow P (A \cap B) = 0 Therefore, P \large(\frac{B}{A}) =$$ \large (\frac{P(A\;\cap\; B)}{P(A)}) = 0$
edited Jun 22, 2013