SOLUTION: The following table lists the joint probabilities associated with smoking and lung disease among 60-to-65 year-old men. |||||||||||||||||||smoker||||non smoker Has lung diseas:

Algebra ->  Probability-and-statistics -> SOLUTION: The following table lists the joint probabilities associated with smoking and lung disease among 60-to-65 year-old men. |||||||||||||||||||smoker||||non smoker Has lung diseas:      Log On


   

Question 1205230: The following table lists the joint probabilities associated with smoking and lung disease among 60-to-65 year-old men.
|||||||||||||||||||smoker||||non smoker
Has lung diseas::::0.1||||||||0.03
No lung disease::::0.16|||||||0.71
One 60-to-65 year old man is selected at random. What is the probability of the following events?

A. He is a smoker:
B. He does not have lung disease:
C. He has lung disease given that he is a smoker:
D. He has lung disease given that he does not smoke
Found 2 solutions by Bogz, math_tutor2020:
Answer by Bogz(13) About Me  (Show Source):
Answer by math_tutor2020(3817) About Me  (Show Source):
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Given table
SmokerNonsmoker
Lung Disease0.10.03
No Lung Disease0.160.71


I'll multiply each of those values in the table by 100
Eg: 0.1*100 = 10
SmokerNonsmoker
Lung Disease103
No Lung Disease1671

That way each value is now a whole number.

Let's compute the row and column totals.
SmokerNonsmokerTotal
Lung Disease10313
No Lung Disease167187
Total2674100

Example: 10+3 = 13 at the end of row 1.

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Part (A)

There are 26 smokers out of 100 men total.
P(smoker) = 26/100 = 0.26

Or alternatively you can add the decimal values along column 1 to get: 0.1+0.16 = 0.26
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Part (B)

87 men do not have lung disease out of 100 total.
P(no lung disease) = 87/100 = 0.87

Or alternatively you can add the decimal values along row 2 to get: 0.16+0.71= 0.87
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Part (C)

"given that he is a smoker" means we know 100% the randomly selected person smokes.
We focus on the "smoker" column only.

Of the 26 total people here, 10 have lung disease.
P(lung disease given smoker) = 10/26 = 5/13 = 0.384615 approximately
It's roughly a 38.46% chance

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Part (D)

This time we focus on the "nonsmoker" column because we're told "given that he does not smoke".

3 nonsmokers have lung disease out of 74 nonsmokers total.
P(lung disease given nonsmoker) = 3/74 = 0.040541 approximately
It's roughly a 4.05% chance