# A coin is tossed

Sample space S={(HHH),(HHT),(HTH),(HTT),(THH),(THT),(TTH),(TTT)}

A={HHH,HTH,HHT,HTT}

B={HHH,HHT,THT,THH}

AB={HHH,HHT}

Therefore A and B are independent events.

(ii) Sample space S={(HHH),(HHT),(HTH),(HTT),(THH),(THT),(TTH),(TTT)}

P(B)={HHH,HHT,THT,THH}

C= exactly two heads are tossed in a row.

P(C)={HHT,THH}

AB={HHT,THH}

Therefore B and C are not independent events.

(iii) Sample space S={(HHH),(HHT),(HTH),(HTT),(THH),(THT),(TTH),(TTT)}

C= exactly two heads are tossed in a row.

C={HHT,THH}

A={HHH,HTH,HHT,HTT}

AB={HHT}

Therefore A and C are independent events.

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