Q. 185.0( 2 Votes )

A coin is tossed thrice and all the eight outcomes are assumed equally likely. In which of the following cases are the following events A and B are independent?
i. A=the first throw results in head, B=the last throw results in tail

ii. A=the number of heads is odd, B=the number of tails is odd

iii. A=the number of heads is two, B=the last throw results in head

Answer :

It is given that the coin is tossed thrice, so the sample space will be,


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


For independent event, P(A)*P(B)=P(AB)


i. A=the first throw results in head, B=the last throw results in tail


A={HHH,HHT,HTH,HTT}



B={HHT,HTT,THT,TTT}



AB={HHT,HTT}





Therefore A and B are independent events.


ii. A=the number of heads is odd, B=the number of tails is odd


A={HTT,THT,TTH}



B={HTH,THH,HHT}



AB={}=Ø



A and B are not independent


iii. A=the number of heads is two, B=the last throw results in head


A={HHT,HTH,THT}



B={HHH,HTH,THH,TTH}



AB={HTH}





Therefore A and B are not independent events.

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