You were watching TV News and the reporter just uttered a politically incorrect

statement (event S). Of course this means she is probably insensitive (event I) or

misinformed (event M). But just how probable is probable? Luckily, you know certain

probabilities: P(I), P(M), P(S | M), P(S | I), P(S | !M), P(S | !I), which are prior

probabilities of reporters being insensitive, being misinformed, and the conditional

probabilities of them uttering politically incorrect statements given that they are

misinformed, insensitive, well-informed, and sensitive.

i) Calculate P(I or M | S), the probability of event 'I or M', in terms of known

priors and conditionals. You may assume that I and M are conditionally

independent given S.

ii) Show that, under the same assumption, P(I or M | S) >= P(I | S). Explain in

words why it must be so.