If a b are two events such that p(a) = 0.2, p(b 0.6 and p(a b) = 0.2 then the value of p(a b) is)

If A and B are events such that P (A) = 0.6, P (B) = 0.3 and P (A ∩ B) = 0.2, find P (A/B) and P (B/A).

\[\text{ Given } : \]\[P\left( A \right) = 0 . 6\]\[P\left( B \right) = 0 . 3 \]\[P\left( A \cap B \right) = 0 . 2\]\[ \text{ Now } , \]\[P\left( \frac{A}{B} \right) = \frac{P\left( A \cap B \right)}{P\left( B \right)}\]\[ \Rightarrow P\left( \frac{A}{B} \right) = \frac{0 . 2}{0 . 3} = \frac{2}{3}\]\[P\left( \frac{B}{A} \right) = \frac{P\left( A \cap B \right)}{P\left( A \right)}\]

\[ \Rightarrow P\left( \frac{B}{A} \right) = \frac{0 . 2}{0 . 6} = \frac{1}{3}\]

Concept: Probability Examples and Solutions

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If A and B are two events such that P (A ∩ B) = 0.32 and P (B) = 0.5, find P (A/B).

\[\text{ Given } : \]\[P\left( B \right) = 0 . 5 \]\[P\left( A \cap B \right) = 0 . 32\]\[\text{ Now } , \]\[P\left( \frac{A}{B} \right) = \frac{P\left( A \cap B \right)}{P\left( B \right)}\]

\[ \Rightarrow P\left( \frac{A}{B} \right) = \frac{0 . 32}{0 . 5} = \frac{32}{50} = 0 . 64\]

Concept: Probability Examples and Solutions

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