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
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(A∩B)
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}
A∩B={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}
A∩B={}=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}
A∩B={HTH}
Therefore A and B are not independent events.
Couldn't generate an explanation.
Generated by AI. May contain inaccuracies — always verify with your textbook.
