(1) Show that the following languages are not regular using Pumping Lemma. L = {ww: wl (a, b)* (2 points) L = {aba: p n+1} (with n 0,10 ) (2 points) (2) 5.2.13 (P145) (2 points) (3) Find a Context free grammar for the language, L = { a" ww b" : w {a, b}*, n 1 (2 points) (4) Suppose that the bowl contains many cookies. Some cookies are colored red and some are colored brown. 45% of the cookies in the bowl contain nuts, and 55% contain chocolate chips. 20% of cookies containing nuts are colored brown. 30% of cookies colored brown. What is the probability that a brown cookie contains nuts? (2 points) ( P (nuts | brown)=?)