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Math Help - Conditional Probability

  1. #1
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    Conditional Probability

    I think that I understand this but I need some clarification before I turn in my work.


    Because of the increasing nuisance of spam e-mail messages, many start-up companies have emerged to develop e-mail filters. One such filter was recently advertised as being 95% accurate. This could mean one of four things.
    (a)95% of the email allowed through is valid,
    (b)95% of spam is blocked,
    (c) of the blocked e-mail is spam, or
    (d) 95% of valid e-mail is allowed through
    Let S denote the event that the message is spam, and let B denote the event that the filter blocks the message. Using these events and their complements, identify each of these four possibilities as a conditional probability.

    Like I said I just need some clarification on how to do this. For (a) I'm pretty sure that the answer is P(Sc|Bc). Sc is the complement of S and Bc is the complement of B (I couldn't figure out how to make those characters correctly on my pc).

    My questions are why is it that Sc goes first? Is it because we know what Sc is or is there some other reason? If I was right then does the value we know always go first when dealing with conditional probability or is this some sort of special condition? Also I have no idea what the | in between the Sc and the Bc is.

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by Paschendale View Post
    One such filter was recently advertised as being 95% accurate. This could mean one of four things.
    (a)95% of the email allowed through is valid,
    (b)95% of spam is blocked,
    (c) of the blocked e-mail is spam, or
    (d) 95% of valid e-mail is allowed through
    Let S denote the event that the message is spam, and let B denote the event that the filter blocks the message.
    I not sure what you want to do.
    But here goes.
    P(S|B) means: The probability that given that a message is blocked then it was spam.

    P(B|S) means: The probability that given that a message is spam then it was blocked.

    P(S^c|B) means: The probability that given that a message is blocked then it was not spam.

    P(B^c|S) means: The probability that given that a message is spam then it was not blocked.

    Can you continue?
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