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Math Help - Conditional Probabilities

  1. #1
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    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.
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  2. #2
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    can anyone solve this?
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  3. #3
    MHF Contributor matheagle's Avatar
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    Is !M the complement of M?

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

    \bigl(I \cup M\bigr) \supset I which implies that P(I \cup M | S) \ge P(I | S)
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  4. #4
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    That's right
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