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Compute the probability of spam emails given that it does not contain the word "promotion’. (iv) (v) Are both events independent? Explain.

Compute the probability of spam emails given that it does not contain the word "promotion’. (iv) (v) Are both events independent? Explain.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Im looking for iv - v. Thanks

Ahmad received 100 emails. 30% of the total emails is spam emails and 70% is desired emails. The percentage of the word 'promotion' that occurs in the spam emails is 80%. While 10% in the desired emails contains the word 'promotion'. (a) (i) Draw the tree diagram for the above problem. (ii) Compute the probability which contains the word 'promotion'. (iii) Compute the probability of desired emails and contains the word 'promotion'. Compute the probability of spam emails given that it does not contain the word "promotion'. (iv) (v) Are both events independent? Explain.
Transcribed Image Text:Ahmad received 100 emails. 30% of the total emails is spam emails and 70% is desired emails. The percentage of the word 'promotion' that occurs in the spam emails is 80%. While 10% in the desired emails contains the word 'promotion'. (a) (i) Draw the tree diagram for the above problem. (ii) Compute the probability which contains the word 'promotion'. (iii) Compute the probability of desired emails and contains the word 'promotion'. Compute the probability of spam emails given that it does not contain the word "promotion'. (iv) (v) Are both events independent? Explain.
Expert Solution
Step 1

Given:

P (S) = 0.30

P (D) = 0.70

P (P| S) = 0.80

P (P | D) = 0.10

Step 2

P (P) = PP|S×PS+PP|D×PD            =0.80×0.30+0.10×0.70            =0.31

Tree diagram

Probability homework question answer, step 2, image 1

iv)

Probability of spam email given it does not have word 'promotion'

P (S |NP)

PNP=1-PP            =1-0.31            =0.69PS|NP=PNP|S×PSPNP                =0.20×0.300.69                =0.0870

The required probability is 0.0870

 

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