The Basic Practice of Statistics
The Basic Practice of Statistics
8th Edition
ISBN: 9781319057916
Author: Moore
Publisher: MAC HIGHER
Question
Book Icon
Chapter 13, Problem 13.47E
To determine

To find: The conditional probability that he or she also smokes cigarettes given that a student smoke electronic cigarette and the conditional probability that he or she also smokes electronic cigarettes given that a student smoke cigarette.

Expert Solution & Answer
Check Mark

Answer to Problem 13.47E

The conditional probability that he or she also smokes cigarettes given that a student smoke electronic cigarette is 0.1875.

The conditional probability that he or she also smokes electronic cigarettes given that a student smoke cigarette is 0.3333.

Explanation of Solution

Given info:

The youth of U.S. has declined cigarette smoking in recent years while the use of some other tobacco products has increased. The high school students used several tobacco products in last 30 days, more than who had used more than half and multiple tobacco products. Let A, B and C denotes the events corresponding to the different types of tobacco products in last 30 days and these are given below:

Events A denotes cigarette, B denotes electronic cigarette and C denotes other tobacco products including cigars, pipes, smokeless tobacco and hookahs.

The probabilities that a randomly selected high school student used these different tobacco products are shown below:

P(A)=0.09 , P(B)=0.16 , P(C)=0.12 , P(AandB)=0.03 , P(AandC)=0.04 , P(BandC)=0.04 and P(AandBandC)=0.01 .

Calculation:

From the given information,

P(A)=0.09 , P(B)=0.16 , P(C)=0.12 , P(AandB)=0.03 , P(AandC)=0.04 , P(BandC)=0.04 and P(AandBandC)=0.01 .

The remaining probabilities are given below:

The probability of (AandBandnotC) is given as,

P(AandBandnotC)=P(A)[P(AandB)+P(AandC)]=0.09[0.03+0.04]=0.090.07=0.02

The probability of (AandnotBandnotC) is given as,

P(AandnotBandnotC)=P(A)[P(AandC)+P(AandBandC)+P(AandBandnotC)]=0.09[0.03+0.01+0.02]=0.090.06=0.03

The probability of (AandCandnotB) is given as,

P(AandCandnotB)=P(AandC)P(AandBandC)=0.040.01=0.03

The probability of (BandAandnotC) is given as,

P(BandCandnotA)=P(BandC)P(AandBandC)=0.040.01=0.03

The probability of (BandnotAandnotC) is given as,

P(BandnotAandnotC)=P(B)[P(AandBandC)+P(AandBandnotC)+P(BandCandnotA)]=0.16[0.01+0.02+0.03]=0.160.06=0.10

The probability of (CandnotAandnotB) is given as,

P(CandnotAandnotB)=P(C)[P(AandBandC)+P(AandCandnotB)+P(BandCandnotA)]=0.12[0.01+0.03+0.03]=0.120.07=0.05

Venn diagram:

The Venn diagram of the events A, B and C and mark the probabilities of all combinations of school students used different tobacco product is given below:

The Basic Practice of Statistics, Chapter 13, Problem 13.47E

Probability:

The conditional probability that he or she also smokes cigarettes given that a student smoke electronic cigarette and the conditional probability that he or she also smokes electronic cigarettes given that a student smoke cigarette are obtained as shown below:

The conditional probability that he or she also smokes cigarettes given that a student smoke electronic cigarette is given as,

P(A|B)=P(AB)P(B)=[P(AandBandC)+P(AandBandnotC)][P(AandBandC)+P(AandBandnotC)+P(BandCandnotA)+P(BandnotAandnotC)]=[0.02+0.01][0.01+0.02+0.03+0.10]=0.030.16=0.1875

Thus, the conditional probability that a student smokes cigarettes given that he or she smokes electronic cigarette is 0.1875.

The conditional probability that a student smokes electronic cigarettes given that he or she smokes cigarette is given as,

P(B|A)=P(AB)P(A)=[P(AandBandC)+P(AandBandnotC)][P(AandBandC)+P(AandBandnotC)+P(AandCandnotB)+P(AandnotBandnotC)]=[0.01+0.02][0.01+0.02+0.03+0.03]=0.030.09=0.3333

Thus, the conditional probability that a student smokes electronic cigarette given that he or she smokes cigarette is 0.3333.

Interpretation:

Among the different types of tobacco products used by the high school students, the percentage of students who smoke cigarette given that electronic cigarette is 18.75% and the percentage of students who smoke electronic cigarette given that smoke cigarette is 33.33%.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
The scores of 8 students on the midterm exam and final exam were as follows.   Student Midterm Final Anderson 98 89 Bailey 88 74 Cruz 87 97 DeSana 85 79 Erickson 85 94 Francis 83 71 Gray 74 98 Harris 70 91   Find the value of the (Spearman's) rank correlation coefficient test statistic that would be used to test the claim of no correlation between midterm score and final exam score. Round your answer to 3 places after the decimal point, if necessary. Test statistic: rs =
Business discuss
Business discuss
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Text book image
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Text book image
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Text book image
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
Text book image
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Text book image
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman