A box contains four tickets numbered 0 1 1 and 2 let sn be

Question

A box contains four tickets, numbered 0, 1, 1, and 2. Let S_n be the sum of the numbers obtained from n draws at random with replacement from the box.

a) Display the distribution of S₂ in a suitable table.

b) Find P(S₅₀ = 50) approximately.

c) Find an exact formula for P(Sn = k) (k = 0, 1, 2, . . ).