Question

An alarming number of U.S. adults are either overweight or obese. The distinction between overweight and obese is made on the basis of body mass index (BMI), expressed as weight/height2. An adult is considered overweight if the BMI is 25 or more but less than 30. An obese adult will have a BMI of 30 or greater. According to a January 2012 article in the Journal of the American Medical Association, 33.1% of the adult population in the United States is overweight and 35.7% is obese. Use this information to answer the following questions.

a. What is the probability that a randomly selected adult is either overweight or obese? (Round your answer to 3 decimal places.)
b. What is the probability that a randomly selected adult is neither overweight nor obese? (Round your answer to 3 decimal places.)
c. Are the events "overweight" and "obese" exhaustive?
A. Yes because you cannot be both overweight and obese.
B. Yes because you can be both overweight and obese.
C. No because you may either be overweight or obese.
D. No because you may be neither overweight nor obese.

Answer 1

a. The probability that a randomly selected adult is either overweight or obese is:

= 68.8%.

b. The probability that a randomly selected adult is neither overweight nor obese is:

= 31.2%

c.

D. No because you may be neither overweight nor obese. The events "overweight" and "obese" are not exhaustive.

Explanation:

Overweight adult = BMI ≥ 25 but < 30

Obese adult = BMI ≥ 30

Journal of the American Medical Association:

Overweight adult population in the United States = 33.1%

Obese adult population in the United States = 35.7%

The probability that a randomly selected adult is either overweight or obese = Percentage of overweight adult population + Percentage of obese adult population

= 33.1% + 35.7%

= 68.8%

The probability that a randomly selected adult is neither overweight nor obese = 1 - 68.8%

= 31.2%

The events "overweight" and "obese" can only be exhaustive if their combined probabilities of occurrence equals 1 or 100%.