Question

According to the nonprofit group Zero Population Growth, 78% of the US population now lives in urban areas. Scientists at Princeton University and the University of Wisconsin report that about 15% of all American adults care for ill relatives. Suppose that 11% of adults living in urban areas care for ill relatives. (Hint: the last sentence is a conditional probability) a. Determine the probability of randomly selecting an adult from the US population who lives in an urban area and is caring for an ill relative. b. What is the probability of randomly selecting an adult from the US population who lives in an urban area and does not care for an ill relative? c. Determine the probability that an adult lives in a nonurban area and cares for an ill relative.

Answer 1

The probability of selecting an adult from the US population who lives in an urban area and is caring for an ill relative is 8.58%. The probability of selecting an urban adult who does not care for an ill relative is 69.42%. The probability that an adult lives in a nonurban area and cares for an ill relative is 3.3%.

Step-by-step explanation:

Calculating Probabilities for Urban and Nonurban Adults Caring for Ill Relatives

Let's solve each part of the question using the information provided and basic principles of probability. We will apply the concept of conditional probability for part (a) which is given by the formula P(A and B) = P(B) × P(A given B).

1. Probability of an adult living in an urban area and caring for an ill relative: Given that 78% of the US population lives in urban areas (urban population probability), and 11% of adults living in urban areas care for ill relatives (conditional probability), the joint probability is P(Urban and Caring) = 0.78 × 0.11 = 0.0858 or 8.58%.
   
2. Probability of an adult living in an urban area and not caring for an ill relative: This can be found by subtracting the probability of caring for an ill relative from the total urban population probability, which is P(Urban and Not Caring) = 0.78 × (1 - 0.11) = 0.78 × 0.89 = 0.6942 or 69.42%.
   
3. Probability of an adult living in a nonurban area and caring for an ill relative: To find this, we need to know the probability of living in a nonurban area (which is 100% - 78% = 22%) and the overall probability that any American adult cares for an ill relative, which is 15%. Since the care in nonurban or urban areas are mutually exclusive events, the probability is P(Nonurban and Caring) = 0.22 × 0.15 = 0.033 or 3.3%.
   

The calculations show the intricate relationship between urbanization and caregiving within American society, highlighting the impact on those living in urban areas versus nonurban areas.