# 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 tailii. A=the number of heads is odd, B=the number of tails is oddiii. A=the number of heads is two, B=the last throw results in head

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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