Questions: A recent study of patients found that of 95 alcoholic patients, 82 had elevated cholesterol levels, and of 305 nonalcoholic patients, 64 had elevated cholesterol levels. If a patient is selected at random, find the probability that the patient is the following. Round your answers to three decimal places. Part 1 of 3 P( alcoholic with elevated cholesterol) = Part 2 of 3 P( nonalcoholic) =

Solution Steps

To find the probability that a randomly selected patient is an alcoholic with elevated cholesterol levels, we use the formula:

$$P(\text{alcoholic with elevated cholesterol}) = \frac{\text{Number of alcoholic patients with elevated cholesterol}}{\text{Total number of patients}} = \frac{82}{400}$$

Calculating this gives:

$$P(\text{alcoholic with elevated cholesterol}) = 0.205$$

To find the probability that a randomly selected patient is nonalcoholic, we use the formula:

$$P(\text{nonalcoholic}) = \frac{\text{Number of nonalcoholic patients}}{\text{Total number of patients}} = \frac{305}{400}$$

Calculating this gives:

$$P(\text{nonalcoholic}) = 0.762$$

Final Answer