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  2. A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event “number is even” and B be the event “number is marked red”. Find whether the events A and B are independent or not.   
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A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event “number is even” and B be the event “number is marked red”. Find whether the events A and B are independent or not. 

 

 

 

 
 
 
 
 

Answers (1)
R Ravindra Pindel

Given : S=\left \{ 1,2,3,4,5,6 \right \}

Let two events be A=\left \{ 2,4,6 \right \}    The number is even

                              B=\left \{ 1,2,3 \right \}  The number is red

P(A)=\frac{3}{6}=\frac{1}{2}

P(B)=\frac{3}{6}=\frac{1}{2}

And  P(A\cap B)=\frac{1}{6}

Now, P(A\cap B)=P(A)\cdot P(B)

Applying the value:     \frac{1}{6}=\frac{1}{2}\cdot \frac{1}{2}

                                \frac{1}{6}\neq\frac{1}{4}

\therefore P(A\cap B)\neq P(A)\cdot P(B)

Hence, A and B are not independent.

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