Question

You are designing a new cloud-based, AI-powered suite of security software for home users. You are currently working on the module to detect phishing and other malicious e-mails. Based on extensive analysis of millions of e-mails you gathered using a bogus Facebook app, you have determined the following:

i. 68% of malicious emails contain the phrase “weird trick”

ii. 3% of valid email messages contain the phrase “weird trick”

iii. 22% of all email messages are malicious

Determine the following probabilities:

a. A message contains the phrase “weird trick”

b. The message is malicious, given that it contains the phrase “weird trick”

c. A message is not malicious, given that it does not contain the phrase “weird trick”

Answer 1

a) P(contains the phrase “weird trick”)=P(malicious and contains the phrase “weird trick”)+P(not malicious and contains the phrase “weird trick”)=0.22*0.68+(1-0.22)*0.03=0.1730

b)

P(malicious|contains the phrase “weird trick”)

=P((malicious and contains the phrase “weird trick”)/P(contains the phrase “weird trick”)

=0.22*0.68/0.1730=0.8647

c)

P(not malicious|not contains the phrase “weird trick”)

=P(not malicious and not contains the phrase “weird trick”)/P(not contains the phrase “weird trick”)

=(1-0.22)*(1-0.03)/(1-0.1730)=0.9149