Problem #1: An email filter is planned to separate valid e-mails from spam. The

Question

Problem #1: An email filter is planned to separate valid e-mails from spam. The wordfree occurs in 78% of the spam messages and only 5% of the valid messages. Also, 11% of the messages are spam (a) If an email message is randomly selected, find the probability that it is spam, given that it contains the word free (b) If an email message is randomly selected, find the probability that it is valid, given that it does not contain the word free Problem #1(a) Answer correct to 4 decimals Problem #1(b): Answer correct to 4 decimals Just Save Submit Problem #1 for Grading Problem #1 | Attempt #1 Attempt #2 | Attempt #3 1(a) 1(b) 1(a) 1(b) Your Answer: 1(a) 1(b) Your Mark:1(a) 1(b 1(a) 1(b 1(a) 1(b

Explanation / Answer

Ans:

valid means that email is not spam

Given that

P(free/spam)=0.78

P(free/not spam)=0.05

P(not free/not spam)=1-0.05=0.95

P(spam)=0.11

P(not spam)=1-0.11=0.89

Now find,P(free)=P(free/spam)*P(spam)+P(free/not spam)*P(not spam)

=0.78*0.11+0.05*0.89=0.1303

P(not free)=1-0.1303=0.8697

a)

P(spam/free)=P(free/spam)*P(spam)/P(free)

=0.78*0.11/0.1303=0.6585

b)

P(not spam/not free)=P(not free/not spam)*P(not spam)/P(not free)

=0.95*0.89/0.8697=0.9722

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