# 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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Guys, does anyone know the answer?

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.

## probability

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

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## 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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## Question : Naive Bayes classifier question

## [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.

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

Guys, does anyone know the answer?