the probability that people show up is given by:
you want the chances of more people showing up than there are seats for. since there are actually 300 seats, but 310 tickets sold, it means we will not have enough seats if 301 people, or 302 people, or ..., 310 people show up. that is, the probability of that happening is:
that gives you your answer.
the calculations here are a bit much, so you may consider using the Normal approximation to the binomial distribution. i think it would be somewhat accurate in this case, since we have a relatively large number of trials, namely 310. do you know how to do the approximation? you have to find the z-score and all that. ring a bell?