Let's say that tomorrow national president election is held. A poll asks 1100 persons which of the two candidates, A or B, will he or she will vote. 750 say will vote A, and 250 say will vote B. What are the chances each will win the election? I think this problem is not the same as choosing a random voter and let him or her decide. Therefore, I assume that the chance A wins elections is higher than 0.75, and closer to 1.
Update: Since the election generated a lot of fuss let me rephrase the question: you have a box containing $N$ white and black balls. From the box you extract $N' <= N$ random balls and count $W$ white balls and $B$ black balls ($W + B = N'$). What is the probability that the box initially contained more white balls than black balls?