What is the probability to receive an e-mail that is spam and contains rar attachment? 00.1118 0.1716 00.0182 00.86
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![What is the probability to receive an e-mail that is spam and contains rar attachment?
00.1118
00.1716
00.0182
00.86](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e67886a-f342-4269-9168-b4ea166f5578%2F7e58f96d-f640-41be-9e78-7436ec4573a5%2Fn0qsq1d_processed.jpeg&w=3840&q=75)
![(Topic: Total Probability and Bayes Theorem)
Over the past year, statistics of all e-mails I received into my inbox were as follows:
• 56% of e-mails contained NO attachments,
• 17% of e-mails contained Microsoft-Word-document attachments,
• 13% of e-mails contained a .rar file attachments, and
• 14% of e-mails contained an .exe file attachments.
Moreover, after inspecting all e-mails, the following further statistics were revealed:
• Out of the e-mails contained no attachments, 97% were legitimate and the remaining ones were spam.
• Out of the e-mails contained MS Word attachments, 53% were legitimate and the remaining ones were
spam.
• Out of the e-mails contained rar attachments, 14% were legitimate and the remaining ones were spam.
• All the e-mails contained exe attachments were spam.
Assume that this year's e-mails will also follow the previous statistics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e67886a-f342-4269-9168-b4ea166f5578%2F7e58f96d-f640-41be-9e78-7436ec4573a5%2F66vdaei_processed.jpeg&w=3840&q=75)
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