Arlen is planning a dinner party at which he will be able to accommodate seven guests. From past experience, he knows that each person invited to the party will accept his invitation with probability 0.5. He also knows that each person who accepts will actually attend with probability 0.8. Suppose that Arlen invites twelve people. Assuming that they behave independently of one another, what is the probability that he will end up with more guests than he can accommodate?

(Hint: Be careful about the inequality in the probability, , for a discrete random variable.)