# Bayes' rule can be used to identify and filter spam emails and text messages.In this collection, 747 of the 5574 total messages (13.40%) are identified as spam. The word “free” is contained in 4.75% of all messages, and 3.57% of all messages both contain the word “free” and are marked as spam. The word “text” (or “txt”) is contained in 7.01% of all messages, and in 38.55% of all spam messages. Of all spam messages, 17.00% contain both the word “free” and the word “text” (or “txt”). Of all non-spam messages, 0.06% contain both the word “free” and the word “text” (or “txt”) . Given that a message contains the word “free” but does NOT contain the word “text” (or “txt”), what is the probability that it is spam?

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Bayes' rule can be used to identify and filter spam emails and text messages.In this collection, 747 of the 5574 total messages (13.40%) are identified as spam. The word “free” is contained in 4.75% of all messages, and 3.57% of all messages both contain the word “free” and are marked as spam. The word “text” (or “txt”) is contained in 7.01% of all messages, and in 38.55% of all spam messages. Of all spam messages, 17.00% contain both the word “free” and the word “text” (or “txt”). Of all non-spam messages, 0.06% contain both the word “free” and the word “text” (or “txt”) . Given that a message contains the word “free” but does NOT contain the word “text” (or “txt”), what is the probability that it is spam?

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Step 1

Given Data

P(Spam) = 0.1340

P(Not spam) = 1- P(spam) = 1 - 0.1340 = 0.866

P(Free) = 0.0475

P(Free and spam) = 0.0357

P(Text) = 0.0701

P(Text and Free if Spam) = 0.17

Step 2

Solving

By Applying conditional probability

Step 3

Now Applying Baye...

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