Case 1 : Arjun tells the truth that India won , then Karan must lie about the fact India lost , in order India to win .
Therefore : (3/4)*(2/3) = (1/2)
Case 2: Arjun is lieing about India's win then karan must also lie about India's loss because the motive is to make India win .
Therefore (1/4)*(2/3) = 1/6 .
Total probability for India wining is 1/2 + 1/6 = 2/3 .
Hence answer is B .