A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A bethe event, the number is even, and B be the event, the number is red. AreA and B independent?

A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A beth

1.	A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A bethe event, the number is even, and B be the event, the number is red. AreA and B independent?
Answer» When a die is thrown, the sample space (S) is `S={1,2,3,4,5,6}` Let A : the number is even `={2,4,6}` `P(A)=3/6=1/2` B : the number is red `={1,2,3}` `P(B)=3/6=1/2` `A nnB={2}` `P(AnnB)=1/6` `P(A).P(B)=1/2xx1/2xx=1/4ne1/6` `impliesP(A).P(B)neP(AB)` Therefore, A and B are not independent.

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A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A bethe event, the number is even, and B be the event, the number is red. AreA and B independent?

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