discrete math need help 4. (6 points) Suppose that a company is developing a web

Question

discrete math need help

4. (6 points) Suppose that a company is developing a web browser which tests web sites for phishing If the website is actually used for phishing, then the browser will detect it with probability 0.9. If the website is not used for phishing the browser may incorrectly identify it as phishing with probability 0.05. Suppose a randomly chosen website is used for phishing with probability 0.01. Let P be the event that a randomly chosen website is used for phishing, and let W be the event that a randomly chosen website has been identified by the web browser as being used for phishing. What is the probability that if a website was reported as being used for phishing that it is actually being used for phishing? That is, what is P(P | W)?

Explanation / Answer

Ans:

P(detect/ phishing)=0.9

P(not detect/phishing)=1-0.9=0.1

P(detect/not phishing)=0.05

P(not detect/not phishing)=1-0.05=0.95

P(phishing)=0.01

P(not phishing)=1-0.01=0.99

P(P/W)=P(phishing/detect)=P(detect /phishing)*P(phishing)/P(detect)

P(detect)=P(detect/phising)*P(phishing)+P(detect/not phishing)*P(not phishing)

=0.9*0.01+0.05*0.99

P(detect)=0.0585

P(P/W)=P(phishing/detect)=(0.9*0.01)/0.0585

                                             =0.1538

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