A coin is tossed thrice. Let the event E be the first throw results in a head and the event F be the last throw results in a tail. Find whether the events E and F are independent.

Explanation

Let `S={{HHH}, {HHT}, {HTH}, {THH}, {T TH}, {THT}, {HT T}, {T T T}}`

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{P}({E})={P}({HHH}, {HHT}, {HTH}, {HTT})=frac{4}{8}=frac{1}{2}`

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{P}({F})={P}({HHT}, {THT}, {HTT}, {TTT})=frac{4}{8}=frac{1}{2}`

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P(E cap F)=P(H H T, H T T)=frac{2}{8}=frac{1}{4}`

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therefore P(E cap F)=P(E) P(F) [because frac{1}{4}=frac{1}{2} times frac{1}{2}]`

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therefore` E and F are independent.