Question

Bayes' rule can be used to identify and filter spam emails and text messages. This question refers to a large collection of real SMS text messages from participating cellphone users.1 In this collection, 747 of the 5574 total messages () are identified as spam. The word "text" (or "txt") is contained in of all messages, and in of all spam messages. What is the probability that a message is spam, given that it contains the word "text" (or "txt")?

Answer 1

Answer:

There is a 13.40% probability that a message is spam, given that it contains the word "text" (or "txt").

Step-by-step explanation:

The problem states that

There are 5574 messages.

There are 747 messages that are spam.

Every message contains the word text.

Bayes rule:

What is the probability of B, given that A?

$P(A/B) = \frac{P(A \cap B)}{P(A)}$

In this problem, we have that

A is containing the word text. So $P(A) = 1$

So

$P(A/B) = \frac{P(A \cap B)}{P(A)} = P(A \cap B)$

$A \cap B$ is containing the word text and being a spam message. So:

$P(A \cap B) = \frac{747}{5574} = 0.1340$

There is a 13.40% probability that a message is spam, given that it contains the word "text" (or "txt").