Question

# Data from Office on Smoking and Health, Centers for Disease Control and Prevention, indicate that 45%...

Data from Office on Smoking and Health, Centers for Disease Control and Prevention, indicate that 45% of adults who did not finish high school, 33% of high school graduates, 24% of adults who completed some college, and 11% of college graduates smoke. Suppose that one individual is selected at random and it is discovered that the individual smokes. Use the probabilities in the following table to calculate the probability that the individual is a college graduate.

 Education Employed Unemployed Not a high school graduate 0.0975 0.0080 High school graduate 0.3108 0.0128 Some college, no degree 0.1785 0.0062 Associate Degree 0.0849 0.0023 Bachelor Degree 0.1959 0.0041 Advanced Degree 0.0975 0.0015

Probability =

Hints: This problem has all the information you need, but not in the typical ready-to-use form. The table above can tell you the proportion of people with various levels of education in the population. Keep in mind that any degree (Associate, Bachelor, or Advanced) counts as graduating from college.

Solution:

This is an introductory-level Bayesian statistics problem.

(0.0975 + 0.008) *0.45 = 0.047475
(0.3108 + 0.0128)*0.33 = 0.106788
(0.1785 + 0.0062)*0.24 = 0.044328
(0.0849 + 0.0023+0.1959+ 0.0041+0.0975+0.0015)*0.11 = 0.042482

Now the proportion of the smoking population is composed of college graduates

0.042482 / (0.042482 + 0.044328 + 0.106788 + 0.047475) = 0.176220

There is approximately an 18% chance that a random individual is a college graduate given that he is a smoker.

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