Q. 43.7( 3 Votes )

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

Answer :

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


A=first toss is head


A={HHH,HTH,HHT,HTT}


B=second toss is head


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)}


B=second toss is head


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=first toss is head


A={HHH,HTH,HHT,HTT}




AB={HHT}





Therefore A and C are independent events.


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