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    a spam filtering system has a probability of 0.95 to correctly classify a mail as spam and 0.10 probability of giving false positives. it is estimated that 1% of the mails are actual spam mails. suppose that the system is now given a new mail to be classified as spam/ not-spam, what is the probability that the mail will be classified as spam?

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    get a spam filtering system has a probability of 0.95 to correctly classify a mail as spam and 0.10 probability of giving false positives. it is estimated that 1% of the mails are actual spam mails. suppose that the system is now given a new mail to be classified as spam/ not-spam, what is the probability that the mail will be classified as spam? from screen.

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    A spam filtering system has a probability of 0.95 to classify correctly a mail as spam and 0.10 probability of giving false positives. It is estimated that 0.5 % of mails are actually spam. Suppos...

    Naive Bayes classifier question [closed]

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    A spam filtering system has a probability of 0.95 to classify correctly a mail as spam and 0.10 probability of giving false positives. It is estimated that 0.5 % of mails are actually spam.

    Suppose that the system is now given a new mail to be classified as spam/not spam. What is the probability that the mail will be classified as spam?

    probability probability-theory naive-bayes Share

    asked Aug 24, 2019 at 14:08

    Techie5879 1,3924 4 silver badges 20 20 bronze badges

    please share your attempt –

    Siong Thye Goh

    Aug 24, 2019 at 14:18

    @SiongThyeGoh This is the first of the kind of question I have attempted of its kind....i dont know how to proceed –

    Techie5879

    Aug 24, 2019 at 14:20

    @Techie5879 Did the answers help? –

    callculus42

    Aug 25, 2019 at 19:16

    @callculus Yes it did ...sorry forgot to upvote, I'll do it now –

    Techie5879

    Aug 25, 2019 at 19:17

    Not problem. Thanks for the very quick reply. –

    callculus42

    Aug 25, 2019 at 19:18

    Add a comment

    2 Answers

    1

    You can make a table. The events are

    S S : Mail is a spam cS cS

    : Mails is classified as a spam.

    The numbers in the brackets indicate the order of entries.

    cS cS ¯ ¯ ¯ ¯ ¯ ¯ S A(3) (4) 0.005(1) S ¯ ¯ ¯ B(5) 0.995(2) C(6) 1

    SS¯cSA(3)B(5)C(6)cS¯(4)0.005(1)0.995(2)1

    ... A spam filtering system has a probability of 0.95 to classify correctly a mail as spam.

    That means that 0.95= A 0.005 ⇒A=... 0.95=A0.005⇒A=...

    and 0.10 probability of giving false positives.

    That means a mail is not a spam but it is classified as a spam with a probability of

    10% 10% : P( S ¯ ¯ ¯ ¯ ∩cS) P( S ¯ ¯ ¯ ¯ ) = B 0.995 =0.1

    P(S¯∩cS)P(S¯)=B0.995=0.1

    It is asked for the value of

    P(cS) P(cS) which is A+B=C A+B=C

    The remaining empty cells can be filled with simplest algebra for further questions.

    Share

    edited Aug 24, 2019 at 14:58

    answered Aug 24, 2019 at 14:53

    callculus42 28.4k4 4 gold badges 24 24 silver badges 40 40 bronze badges Add a comment 1 Guide: Let A A

    denote the event that is is really a spam.

    Let B B

    be the event that a mail is classified as a spam.

    You are given P(B|A) P(B|A) and P(B| A c ) P(B|Ac) and also P(A) P(A) .

    Use the law of total probability to compute

    P(B) P(B) . Share

    answered Aug 24, 2019 at 14:29

    Siong Thye Goh 145k20 20 gold badges 83 83 silver badges 146 146 bronze badges Add a comment

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    [Solved] A spam filtering system has a probability of 0.95 to classify correctly a mail as spam and 0.10 probability of giving false positives. It is

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    A spam filtering system has a probability of 0.95 to classify correctly

    a mail as spam and 0.10 probability of giving false positives. It is estimated that 0.5% of the mails are actual spam mails.

    i) Suppose that the system is now given a new mail to be classified as spam/ not-spam, what is the probability that the mail will be classified as spam?

    ii) Find the probability that, given a mail classified as spam by the system, the mail actually being spam.

    iii) Given that a mail is classified as not spam, what is the probability of the mail actually being not spam?

    iv) Find the probability that the mail is misclassified.

    Math Statistics and Probability

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    "sir the answer of part 4 is wrong correct answer is 0.9975"

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