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) =

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) =

Transcript text: 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

Solution Steps

Step 1: Calculate \( P(\text{alcoholic with elevated cholesterol}) \)

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:

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

Step 2: Calculate \( P(\text{nonalcoholic}) \)

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:

\[ P(\text{nonalcoholic}) = 0.762 \]