A die is thrown once. E is the event the number appearing is a multiple of 3 and F is the event the number appearing is even: Are the events E and F independent?

Explanation

`S={1,2,3,4,5,6}`

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E={3,6}, F={2,4,6}, E cap F={6}`

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therefore P(E)=frac{2}{6}=frac{1}{3}, P(F)=frac{3}{6}=frac{1}{2}, P(E cap F)=frac{1}{6}`

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P(E and F)=frac{1}{6}=frac{1}{3} times frac{1}{2}=P(E) times P(F)`

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therefore` E and F are independent events.