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:

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) (Show Source): You can put this solution on YOUR website!
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Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Given table

Smoker Nonsmoker
Lung Disease 0.1 0.03
No Lung Disease 0.16 0.71

I'll multiply each of those values in the table by 100
Eg: 0.1*100 = 10

Smoker Nonsmoker
Lung Disease 10 3
No Lung Disease 16 71

That way each value is now a whole number.

Let's compute the row and column totals.

Smoker Nonsmoker Total
Lung Disease 10 3 13
No Lung Disease 16 71 87
Total 26 74 100

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

------------------------------------------------
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
------------------------------------------------
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
------------------------------------------------
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

------------------------------------------------
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

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	Smoker	Nonsmoker	Total
Lung Disease	10	3	13
No Lung Disease	16	71	87
Total	26	74	100