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A die marked 1, 2, 3 in red and 4, 5, 6 ...

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

Text Solution

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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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