HMMT 2006 U42

Suppose hypothetically that a certain, very corrupt political entity in a universe holds an election with two candidates, say $A$ and $B$. A total of $5,825,043$ votes are cast, but, in a sudden rainstorm, all the ballots get soaked. Undaunted, the election officials decide to guess what the ballots say. Each ballot has a $51 \%$ chance of being deemed a vote for $A$, and a $49 \%$ chance of being deemed a vote for $B$. The probability that $B$ will win is $10^{-X}$. What is $X$ rounded to the nearest 10 ?