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Problem 3: In a certain population, 80% drinks, 15% smokes, and 13% both drinks and smokes. A subject is chosen at random from this population. Events: D Drinks, S Smokes, DS-Drinks and Smokes (a) Fill in the following blanks and use these yalues to complete the table below. Probabilities: P(D) 030 P(S)-O5, P(DS) =0,13 Probabilities Smokes (S) P(DS) Not Smokes (S) Total Drinks (D) O.13 P(DS) = O.67 P(D) = 0.80 %3D Not Drink (D) P(DS)= P(DS)= P(D)= O.2 0.02 P(S) = 0.15 (b) What is the probability the person does not drink? 0.18 P(S) =-0.15 0.85 1-(D) = -0.80 =0.2 %3D %3D Total 1.00 %3D (c) What is the probability the person drinks or smokes? P(DUS)- Plous) = P()t P(S)-P(D5)= 0.80 +0.1S -O,13=0 %3D (d) If the person drinks, what is the probability that he or she smokes? P(8/D)= P(SD/P(D)= 0.13/0.80 = 0,1625 %3D %3D (e) If the person does not smoke, what is the probability that he or she drinks? P(p137= 0.67/0.85 = 0.T882 P(D5)/P(S) = %3D %3D (f) Are the events "Drinks" and "Smokes" mutually exclusive? (State "Yes" or No" and explain.) NO They can both happen at the same time since P(DS)= (g) Are the events "Drinks" and "Smokes" independent? (State "Yes" or No" and explain.) NO P(O) # P(O) P() [0.80 7(0.80).15)=0.12 %3D

Problem 3: In a certain population, 80% drinks, 15% smokes, and 13% both drinks and smokes. A subject is chosen at random from this population. Events: D Drinks, S Smokes, DS-Drinks and Smokes (a) Fill in the following blanks and use these yalues to complete the table below. Probabilities: P(D) 030 P(S)-O5, P(DS) =0,13 Probabilities Smokes (S) P(DS) Not Smokes (S) Total Drinks (D) O.13 P(DS) = O.67 P(D) = 0.80 %3D Not Drink (D) P(DS)= P(DS)= P(D)= O.2 0.02 P(S) = 0.15 (b) What is the probability the person does not drink? 0.18 P(S) =-0.15 0.85 1-(D) = -0.80 =0.2 %3D %3D Total 1.00 %3D (c) What is the probability the person drinks or smokes? P(DUS)- Plous) = P()t P(S)-P(D5)= 0.80 +0.1S -O,13=0 %3D (d) If the person drinks, what is the probability that he or she smokes? P(8/D)= P(SD/P(D)= 0.13/0.80 = 0,1625 %3D %3D (e) If the person does not smoke, what is the probability that he or she drinks? P(p137= 0.67/0.85 = 0.T882 P(D5)/P(S) = %3D %3D (f) Are the events "Drinks" and "Smokes" mutually exclusive? (State "Yes" or No" and explain.) NO They can both happen at the same time since P(DS)= (g) Are the events "Drinks" and "Smokes" independent? (State "Yes" or No" and explain.) NO P(O) # P(O) P() [0.80 7(0.80).15)=0.12 %3D

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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I have a question on part (f) and (g) on this problem

Problem 3: In a certain population, 80% drinks, 15% smokes, and 13% both drinks and smokes. A subject is chosen at random from this population. Events: D= Drinks, S Smokes, DS = Drinks and Smokes (a) Fill in the following blanks and use these yalues to complete the table below. Probabilities: P(D) 0,30 P(S) Q 5 P(DS) = O, \3 Probabilities %3D %3D %3D Smokes (S) Not Smokes (S) P(DS) = Total Drinks (D) P(DS) %3D O.13 O.67 P(D) = 0.80 %3D %3D Not Drink (D) P(DS)= P(DS) = P(D)= 0.2 0.02 P(S) = 0.15 %3D 0.18 P(S) = -0.1530.85 %3D Total 1.00 %3D (b) What is the probability the person does not drink? P. P(D) = 1-0.80 = 0.2 %3D (c) What is the probability the person drinks or smokes? P(oUS)- PloU'S) = P(D)t P(S) -P(D5)= 0.80 +0.1S - 0,13=0,82 %3D (d) If the person drinks, what is the probability that he or she smokes? P8/D)= P(SD/(D)= 0.13/0.80 = 0,1625 %3D (e) If the person does not smoke, what is the probability that he or she drinks? P(PIS7= P(D5/)= 0.67/0.85 = 0.1882 O.67/0.85 = 0. 7882 %3D (f) Are the events "Drinks" and "Smokes" mutually exclusive? (State "Yes" or No" and explain.) (g) Are the events "Drinks" and "Smokes" independent? (State "Yes" or No" and explain.) NO, P(oS # P(O) P() [0.80 #(0.807(0.15)=0.12]
Transcribed Image Text:Problem 3: In a certain population, 80% drinks, 15% smokes, and 13% both drinks and smokes. A subject is chosen at random from this population. Events: D= Drinks, S Smokes, DS = Drinks and Smokes (a) Fill in the following blanks and use these yalues to complete the table below. Probabilities: P(D) 0,30 P(S) Q 5 P(DS) = O, \3 Probabilities %3D %3D %3D Smokes (S) Not Smokes (S) P(DS) = Total Drinks (D) P(DS) %3D O.13 O.67 P(D) = 0.80 %3D %3D Not Drink (D) P(DS)= P(DS) = P(D)= 0.2 0.02 P(S) = 0.15 %3D 0.18 P(S) = -0.1530.85 %3D Total 1.00 %3D (b) What is the probability the person does not drink? P. P(D) = 1-0.80 = 0.2 %3D (c) What is the probability the person drinks or smokes? P(oUS)- PloU'S) = P(D)t P(S) -P(D5)= 0.80 +0.1S - 0,13=0,82 %3D (d) If the person drinks, what is the probability that he or she smokes? P8/D)= P(SD/(D)= 0.13/0.80 = 0,1625 %3D (e) If the person does not smoke, what is the probability that he or she drinks? P(PIS7= P(D5/)= 0.67/0.85 = 0.1882 O.67/0.85 = 0. 7882 %3D (f) Are the events "Drinks" and "Smokes" mutually exclusive? (State "Yes" or No" and explain.) (g) Are the events "Drinks" and "Smokes" independent? (State "Yes" or No" and explain.) NO, P(oS # P(O) P() [0.80 #(0.807(0.15)=0.12]
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