A teacher is distributing sweatshirts to each of the 261 students enrolled in the class. 87 of them wear small, 87 of them wear medium, and 87 of them wear large, so that's the number of sweatshirts of each size we had made. Rather than giving everyone the properly sized sweatshirt, however, each student is being randomly paired with one, where all possible pairings are equally likely.  Recall that I_j​ indicates whether student j gets the correctly sized sweatshirt and A_j​ is the event that student j gets the correctly sized sweatshirt. Answer each of the following questions without relying on any algebra. Intuitively explain why P(A_1A_261) is just slightly larger than P(A_1A_2). Intuitively explain why Cov(I_1​,I_2​) is very slightly negative. Intuitively explain why Cov(I_1,I_261) is very slightly positive. Your answers to each of these three questions are free response and therefore can't be auto-graded. That means we'll be reviewing your answers, so provide clear and convincing arguments without relying on algebra.