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) =
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Solution

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Solution Steps

Step 1: Calculate P(alcoholic with elevated cholesterol) 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(alcoholic with elevated cholesterol)=Number of alcoholic patients with elevated cholesterolTotal number of patients=82400 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(alcoholic with elevated cholesterol)=0.205 P(\text{alcoholic with elevated cholesterol}) = 0.205

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

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

P(nonalcoholic)=Number of nonalcoholic patientsTotal number of patients=305400 P(\text{nonalcoholic}) = \frac{\text{Number of nonalcoholic patients}}{\text{Total number of patients}} = \frac{305}{400}

Calculating this gives:

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

Final Answer

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

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

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