Size of cuts in graphs drawn from $ G_{n,1/2}$
Perhaps what's implicit after "there are" is "asymptotically almost surely", which means that the property holds with probability tending to 1 as n tends to infinity; this is stronger than "in expectation".  You might want to check out a standard textbook on random graphs (e.g. by Alon-Spencer, Bollobas, or Janson-Luczak-Rucinski).