Question

Suppose that 3% of all adults suffer from diabetes and that 31% of all adults are obese. Suppose also that 2% of all adults both are obese and suffer from diabetes. What is the probability that a randomly chosen adult is obese given that he or she suffers from diabetes?

Answer 1

The probability that a randomly chosen adult is obese given that he or she suffers from diabetes is 0.67 or 67%.

Step-by-step explanation:

To find the probability that a randomly chosen adult is obese given that he or she suffers from diabetes, we can use conditional probability. The conditional probability of event A given event B is calculated using the formula: P(A|B) = P(A and B) / P(B).

In this case, we want to find the probability that an adult is obese (event A) given that they suffer from diabetes (event B). The given information tells us that 3% of all adults suffer from diabetes (P(B) = 0.03) and 2% of all adults both are obese and suffer from diabetes (P(A and B) = 0.02).

Using the formula: P(A|B) = P(A and B) / P(B), we can substitute the given values to calculate the probability:

P(A|B) = 0.02 / 0.03 = 2/3 = 0.67 or 67%