bowl 1 contains 10 plain cookies and 30 chocolate chip cookies. bowl 2 contains 20 plain cookies and 20 chocolate chip cookies. an experiment is conducted as follows: (i) a bowl is selected at random, with either being equally probable, and (ii) a cookie from within the chosen bowl is selected at random with each being equally probable. a) what is the probability that a plain cookie is selected given that bowl 1 is selected? b) what is the probability that a plain cookie is selected? c) what is the probability that bowl 1 was selected given that a plain cookie has been selected