Three coins are tossed simultaneously. Consider the event E three heads or three tails, F at least two heads and G at most two heads. Of the pairs (EE), (E, G) and (F,G), which are independent? Which are dependent?

Explanation

Let S={HHH,HHT,HTH,THH,HTT,THT,TTH,TTT}
E={HHH,TTT}

F=(HHH,HTH,HHT,THH}

G=(HHT,HTH,THH,HTT,THT,TTH,TTT}

so E∩F={HHH}

E∩G={TTT}

F∩G={HHT,HTH,THH}

So,`P(E)=2/8,P(F)=4/8,P(G)=7/8`

and` P(E∩F)=1/8,P(E∩G)=1/8,P(F∩G)=3/8`

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