Problem 1. In a study of the relationship between health risk and income, a larg

Question

Problem 1. In a study of the relationship between health risk and income, a large group of people living in MA were asked a series of questions. Some of the results are shown in the following table Income 298 Don't Smoke 20191601 2620 1899 Health Risk Low Medium High Total 257 1156 19785598 22356754 Smoke 601 Total (a) What is the probability that someone in this study smokes? (b) What is the conditional probability that someone in this study smokes, given that the person has high income? (c) What is the probability that someone both smokes and has high income? (Use the Multiplication Rule) (d) What is the probability that someone either smokes or has low income? (Use the Addition Rule)

Explanation / Answer

a)P(smokes)=1156/6754=0.1712

b)

P(Smokes|high incomes)=257/2235=0.1150

c)

P(smokes and high incomes)=P(high income)*P(Smokes|high incomes)=(2235/6754)*(257/2235)

=0.0381

d)

P(either smoke or low income)=P(smoke)+P(low income)-P(smoke and low income)

=(1156+2620-601)/6754=0.4701

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