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Lavanya and Ketak each flip a fair coin (i.e., both heads and tails have equal probability of appearing) $n$ times. What is the probability that Lavanya sees more heads than Ketak?

In the following, the binomial conefficient $n\choose k$ counts the number of $k$-element subsets of an $n$-element set.

(A) $\frac{1}{2}$

(B) $\frac{1}{2}(1 – \sum_{i=0}^{n}\frac{{n\choose i}^2}{2^{2n}})$

(C) $\frac{1}{2}(1 – \sum_{i=0}^{n}\frac{{n\choose i}}{2^{2n}})$

(D) $\frac{1}{2}(1 – \sum_{i=0}^{n}\frac{1}{2^{2n}})$

(B) $\sum_{i=0}^{n}\frac{{n\choose i}}{2^{2n}}$
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