In a game a coin is tossed 2n+m times and a player wins if he does not get any two consecutive outcomes same for atleast 2n times in a row. The probability that player wins the game is

Question : In a game a coin is tossed 2n+m times and a player wins if he does not get any two consecutive outcomes same for atleast 2n times in a row. The probability that player wins the game is

(A) \dfrac{m+2}{2^{2n}+1}

(B) \dfrac{2n+2}{2^{2n}}

(C) \dfrac{2n+2}{2^{2n+1}}

(D) \dfrac{m+2}{2^{2n}}

Answer : option (D)

Solution :

In a game a coin is tossed 2n+m times and a player wins if he does not get any two consecutive outcomes same for atleast 2n times in a row. The probability that player wins the game is
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