Spam Emails. Businesses often use spam email for advertisements because the cost per email is incredibly low and many emails can be sent out at the same time. However, some spam emails, known as phishing emails, may be a malicious attempt to gain access to your computer. Spam emails can be dangerous as they may include malicious links that can infect your computer with malware. Dangerous spam emails often sound urgent and make you feel the need to act. In February 2021, an online article published statistics on spam emails to highlight the severity of the issue. This article reports on the numbers, percentages, and losses caused by spam emails.

a. The article states that nearly 85% of all emails that an email inbox receives are spam. Suppose that 73% of these emails are phishing emails and that not all spam emails will automatically go to an email account’s spam folder. Suppose that 5% of the emails in the spam folder are not spam but have been sent to the spam folder by mistake and that 1% of the spam emails that did not go to the spam folder are phishing emails. What is the probability that a spam email not sent to the spam folder is a phishing email? Apply Bayes’ Rule to obtain your answer.

b. The article also reports that out of all courier services, DHL has received the most phishing emails. Assume that 95% of all spam emails received by DHL went into the spam folder and that 20% of the emails that went into the spam folder were not phishing emails. Concurrently, 10% of the spam emails that did not go into the spam folder were phishing emails. If a random email is selected from DHL’s inbox, what is the probability that the email is a spam email but did go to the spam folder given that it is a phishing email?