Question

Google has hired you to develop an algorithm to detect spam emails. You have the following information for a user: a) Of all the emails she has previously sent to ‘spam’, 85% include the term “Check this out…”; b) Of all her ‘non-spam’ emails 10% include the term “Check this out…”; c) She sends 15% of all emails she receives to spam. What would be your rational guess about the probability that an email containing “Check this out...” is spam?

	a.	One-third
	b.	Half
	c.	Three-fifth
	d.	None of the above

Answer 1

Option (c).

Probability table as follows.

	Spam	Not spam	Total
Includes "Check this"	15% x 85% = 12.75%	85% x 10% = 8.5%	12.75 + 8.5 = 21.25%
Doesn't include "Check this"	15 - 12.75 = 2.25%	85 - 8.5 = 76.5%	2.25 + 76.5 = 78.75%
Total	15%	100 - 15 = 85%	100%

So,

Probability that an email containing “Check this" is spam = 12.75% / 21.25% = 0.6 = 3/5