# A coin is tossed three times. Let the events A,B and C be defined as follows:A=first toss is head, B=second toss is head, and C= exactly two heads are tossed in a row.Check the independence of (i) A and B(ii) B and C(iii) C and A

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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