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SELF DOUBT

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TIFR2011-A-6  IN THIS QUESTION WE GET ANSWER 6 BY THIS METHOD . SIMPLE AND STRAIGHT

OKK WHEN I APPLY THIS METHOD HERE Expectated no of coin toss 

THEN I GET X= 1/2 (X +1 ) + 1/4 (X+2 )  (HH CASE)   + 1/2 (4 )

Which makes X=6 but answer is 4 .where am i wrong

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