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Math Help - probability question?

  1. #1
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    probability question?

    it has been observed that 45% of the email sent to your account is spam and as a result you have set up a spam filter.however the filter fails to quarantine 2% of spam emails and inadvertently quarantines 5% of genuine emails.
    1)what is the probabilty that an email will be quarantined as spam?
    2)if an email is quarantined as spam what is the probabilty that it is actually a spam email?

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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: probability question?

    Quote Originally Posted by university View Post
    1)what is the probabilty that an email will be quarantined as spam?
    p = 98/100 * 45 + 5/100 * 55

    = 44.1 + 2.75

    = 46.85 %
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  3. #3
    MHF Contributor alexmahone's Avatar
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    Re: probability question?

    Quote Originally Posted by university View Post
    2)if an email is quarantined as spam what is the probabilty that it is actually a spam email?
    Using Bayes' theorem,

    P(spam | quarantined as spam) = P(quarantined as spam | spam)P(spam)/P(quarantined as spam) = .98 * .45 / .4685 = .9413 = 94.13 %
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