I need the complete working solutions and accurate answers to this question. Tha
ID: 3272938 • Letter: I
Question
I need the complete working solutions and accurate answers to this question. Thanks
Your e-mail provider has a very good spam filter that only 1.5% of all e-mails passed the filter are spam. A lot of spam e-mails are trying to phish for your personal information so they ask you to go to an unknown web site where you are asked to enter this information. About 98% of the spam email will ask you to click on a link without providing you with the explicit url. In addition, 3% of the legitimate e-mails will ask you to click on a link without the explicit url being shown. For a random e-mail in your inbox (so this email has passed the filter), if you are provided a link without the explicit url, what is the probability that the e-mail is spam? Why is your answer counterintuitive?Explanation / Answer
Here we are given that only 1.5% of the emails that passes the filter are spam. Therefore the probability that an email is a spam given that it is passed through the filter is given as 0.015
Also given that an email is spam, probability that it will ask to click on a link without providing explicit content for it is given as:
P( Click | Spam ) = 0.98
Also we are given that P( Click | Legit ) = 0.03
Now here we have to find the probability that the email is a spam given that it has provided a link without the explicit URL. So we have to compute P( Spam | Click )
Now total probability of Click is first computed as:
P( Click ) = P( Click | Spam ) P(Spam ) + P( Click | Legit ) P(Legit )
P( Click ) = 0.98*0.015 + 0.03*0.985 = 0.04425
Now the required probability P( Spam | Click ) is computed using the Bayes conditional probability formula as:
P( Spam | Click )P(Click ) = P( Click | Spam ) P(Spam )
Putting all the values we get:
P( Spam | Click )*0.04425 = 0.98*0.015
Therefore we get: P( Spam | Click ) = 0.98*0.015/0.04425 = 0.3322
Therefore 0.3322 is the required probability here.