Question

how do you find P(S)??

collection of real SMS text messages from partici- pating cellphone users.13 In this collection, 747 of the 5574 total messages (13.40%) are identified as spam. 11.60 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"? t 11.61 The word "text" (or "xt") is contained in 7.01% of all messages, and in 38.55% of all spam messages. What is the probability that a message is spam, given that it contains the word "text" (or txt")? 11.62 Of all spam messages, 17.00% contain both the word "free" and the word text" (or "txt"). For example, "Congrats!! You are selected to receive a free camera phone, tto claim your prize." Of all non-spam messages, 0.06% contain both the word "free" and the word "text" (or "txt"). Given that a message contains both the word "free" and the word text" (or "txt"), what is the probability that it is spam? 11.63 Given that a message contains the word free" but does NOT contain the word text" (or

Answer 1

P(S) = Probability of identifying a spam message = 747/5574 = 0.134.