Question 1205230
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Given table
<table border = "1" cellpadding = "5"><tr><td></td><td>Smoker</td><td>Nonsmoker</td></tr><tr><td>Lung Disease</td><td>0.1</td><td>0.03</td></tr><tr><td>No Lung Disease</td><td>0.16</td><td>0.71</td></tr></table>


I'll multiply each of those values in the table by 100
Eg: 0.1*100 = 10
<table border = "1" cellpadding = "5"><tr><td></td><td>Smoker</td><td>Nonsmoker</td></tr><tr><td>Lung Disease</td><td>10</td><td>3</td></tr><tr><td>No Lung Disease</td><td>16</td><td>71</td></tr></table>
That way each value is now a whole number.


Let's compute the row and column totals.
<table border = "1" cellpadding = "5"><tr><td></td><td>Smoker</td><td>Nonsmoker</td><td>Total</td></tr><tr><td>Lung Disease</td><td>10</td><td>3</td><td>13</td></tr><tr><td>No Lung Disease</td><td>16</td><td>71</td><td>87</td></tr><tr><td>Total</td><td>26</td><td>74</td><td>100</td></tr></table>
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
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