1. ## Conditional Probabilities

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.

2. can anyone solve this?

3. Is !M the complement of M?

Do you want to show that $\displaystyle P(I \cup M | S) \ge P(I | S)$ ?

$\displaystyle \bigl(I \cup M\bigr) \supset I$ which implies that $\displaystyle P(I \cup M | S) \ge P(I | S)$

4. That's right