Question

Suppose that 3% of all adults suffer from diabetes and that 31% of all adults are obese. Suppose also that 1% of all adults both are obese and suffer fromdiabetes.(a) Find the probability that a randomly chosen adult who is obese also suffers fromdiabetes. Round your answer to the nearest hundredth.(b) Find the probability that a randomly chosen adult is obese, given that he or she suffersfrom diabetes. Round your answer to the nearest hundredth.

Answer 1

a) We already know the chosen adult is obese.

So we need to find this probability:

P(diabetes | obese) = P(diabetes ∩ obese) / P(obese)

In this case, we have:

P(diabetes ∩ obese) = 1% = 0.01

P(obese) = 31% = 0.31

Therefore, this gives us:

P(diabetes | obese) = 0.01/0.31 = 1/31 ≅ 0.03

b) Now we already know the adult suffers from diabetes, and we need to find the following probability:

P(obese| diabetes) = P(diabetes ∩ obese) / P(diabetes)

We have:

P(diabetes) = 3% = 0.03

So, we find:

P(obese| diabetes) = 0.01/0.03 = 1/3 ≅ 0.33