In a given city, either physical or virtual, ten people have a reservation

price for T$-$shirts of a given type equal to $ $11$ and five people have a reservation price

of $ $7.$ Let us suppose that there are two T$-$shirts available; both T$-$shirts are produced

at no cost$.$

Let us suppose that the T$-$shirts are assigned by a dictator $-$ or a bureaucrat or administrator of some sort $-$ according to criteria that from our point of view can be viewed as $$random$.$ In particular, all individual, regardless of their WTPs$,$ can receive the

first T$-$shirt with the same probability, and can then receive the second T$-$shirt, again with the same probability, if they have not received the first one. What is the expected post$-$assignment social surplus?