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  • A die, whose faces are marked 1, 2, 3 in red and 4, 5, 6 in green, is tossed.Let A be the event ‘‘number obtained is even’’ and B be the event‘‘number obtained is red’’. Find if A and B are independent ev

A die, whose faces are marked 1, 2, 3 in red and 4, 5, 6 in green, is tossed.Let A be the event ‘‘number obtained is even’’ and B be the event‘‘number obtained is red’’. Find if A and B are independent events.

 

 

 

 
 
 
 
 

Answers (1)

Since , A be the event of number obtained is even then A= \left \{ 2,4,6 \right \} and B be the event of number obtained is red then A= \left \{ 2,4,6 \right \}
and B be the event of number obtained is red then, B= \left \{ 1,2,3 \right \}
\therefore A\cap B= \left \{ 2 \right \}
so p\left ( A \right )= \frac{3}{6}= \frac{1}{2}         p\left ( B \right )= \frac{3}{6}= \frac{1}{2}\; ;\; p\left ( A\cap B \right )= \frac{1}{6}
Now p\left ( A\cap B \right )\neq p\left ( A \right )\cdot p\left ( B \right )
\frac{1}{6}\neq \frac{1}{4}
Hence the event A and B are not independent events

Posted by

Ravindra Pindel

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