In a study of the relationship between health risk and income, a large group of

Question

In a study of the relationship between health risk and income, a large group of people living in Massachusetts were asked a series of questions. Some of the results are shown in the table.

Income Low Medium High Total

Smoke 634 332 247 1213

Don't smoke 1846 1622 1868 5336

Total 2480 1954 2115 6549

(a) What is the probability that someone in this study doesn't smoke?

(b) What is the probability that someone in this study has low income?

(c) What is the probability that someone in this study either smokes or has low income or both?

(d) What is the probability that someone in this study smokes and has low income?

(e) What is the probability that someone in this study smokes given that he has low income?

(f) What is the probability that someone in this study doesn't smoke given that he has medium income?

Explanation / Answer

Note - I will be rounding all the probabilities to 4 decimal places. If exact answer required please refer to the proportion just before that decimal approximation.

a) P(Doesn't smoke) = 5336/6549 = 0.8148

b) P(Low income) = 2480/6549 = 0.3787

c) P(Smokes or low income or both) = 1213/6549 + 2480/6549 - 634/6549 = 3059/6549 = 0.4671

d) P(Smokes and low income) = 634/6549 = 0.0968

e) P(Smokes | Low income) = 634/2480 = 317/1240 = 0.2556

f) P(Doesn't smoke | Medium income) = 1622/1954 = 811/977 = 0.8301

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