Module Knowledge Check
Question 14
Hailey
Suppose that $3 \%$ of all adults suffer from diabetes and that $28 \%$ of all adults are obese. Suppose also that $2 \%$ of all adults both are obese and suffer from diabetes.
Answer the questions below. (If necessary, consult a list of formulas.)
(a) Find the probability that a randomly chosen adult is obese, given that he or she suffers from diabetes. Round your answer to 2 decimal places.
(b) Find the probability that a randomly chosen obese adult suffers from diabetes. Round your answer to 2 decimal places.
Answer
Final Answer: (a) The probability that a randomly chosen adult is obese, given that he or she suffers from diabetes is \(\boxed{0.67}\). (b) The probability that a randomly chosen obese adult suffers from diabetes is \(\boxed{0.07}\).
Step 1 ：Let's denote the event that an adult is obese as O and the event that an adult suffers from diabetes as D. The problem provides us with the following probabilities: P(D) = 0.03, P(O) = 0.28, and P(O ∩ D) = 0.02.
Step 2 ：We can calculate the probability that a randomly chosen adult is obese, given that he or she suffers from diabetes using the formula for conditional probability: P(O|D) = P(O ∩ D) / P(D). Substituting the given values, we get P(O|D) = 0.02 / 0.03 = 0.67.
Step 3 ：Similarly, we can calculate the probability that a randomly chosen obese adult suffers from diabetes using the formula for conditional probability: P(D|O) = P(O ∩ D) / P(O). Substituting the given values, we get P(D|O) = 0.02 / 0.28 = 0.07.
Step 4 ：Final Answer: (a) The probability that a randomly chosen adult is obese, given that he or she suffers from diabetes is \(\boxed{0.67}\). (b) The probability that a randomly chosen obese adult suffers from diabetes is \(\boxed{0.07}\).
