Bayes’ rule can be used to identify and filter spam emails and text messages. A large collection of real SMS text messagesfrom participating cellphone used in this research. In this collection, 747 of the 5574 total messages (13.40%) are identified as spam.2.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.a)What is the probability that a message contains the word “free”, given that it is spam?b)What is the probability that a message is spam, given that it contains the word “free”?

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Asked Feb 8, 2019
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Bayes’ rule can be used to identify and filter spam emails and text messages. A large collection of real SMS text messagesfrom participating cellphone used in this research. In this collection, 747 of the 5574 total messages (13.40%) are identified as spam.

2.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.a)What is the probability that a message contains the word “free”, given that it is spam?b)What is the probability that a message is spam, given that it contains the word “free”?

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Expert Answer

Step 1

Given  probabilites

P(Spam) = 747/5574 = 0.134

P(free) = 0.0475

P(free and spam)=0.0357

We need to find probability that message contain word free given that it is spam P(free|spam)

Step 2

If A and B are two events then conditional probability P(A|B) is given by the below mentioned formula

So using the formula we compute for probability that a message contains word free given that it is ...

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