If P\left ( A \right )= 0\cdot 6,P\left ( B \right )= 0\cdot 5\; and\; P\left ( \frac{B}{A} \right )= 0\cdot 4,\; find\; P\left ( A\cup B \right )\; and\; P\left ( A\mid B \right ).

 

 

 

 
 
 
 
 

Answers (1)

As P\left ( B\cap A \right )= P\left ( \frac{B}{A} \right )\times P\left ( A \right )= 0\cdot 4\times 0\cdot 6= 0\cdot 24
That is P\left ( A\cap B \right )= 0\cdot 24
Now P\left ( \frac{A}{B} \right )= \frac{P\left ( A\cap B \right )}{P\left ( B \right )}= \frac{0\cdot 24}{0\cdot 5}= \frac{24}{50}= 0\cdot 48
Also P\left ( A\cup B \right )= P\left ( A \right )+P\left ( B \right )-P\left ( A\cap B \right )
                               = 0\cdot 6+0\cdot 5-0\cdot 24= 0\cdot 86

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