Question

A recent study of 300 patients found that of 100 alcoholic patients, 87 had elevated cholesterol levels, and of 200 nonalcoholic patients, 43 had elevated cholesterol levels. If a patient is selected at random, find the probability that the patient is the following.

An alcoholic with elevated cholesterol level

A nonalcoholic

A nonalcoholic with non-elevated cholesterol level

Answer 1

$$P(A)=\dfrac{100}{300}=\dfrac{1}{3}$$

$$P(\bar{A})=1-P(A)=\dfrac{2}{3}$$

$$P(Ch|A)=\dfrac{87}{100}=0.87$$

$$P(Ch|\bar{A})=\dfrac{43}{200}=0.215$$

a)

$$P(A\cap Ch)=P(A)P(Ch|A)=\dfrac{1}{3}(0.87)=0.29$$

b)

$$P(\bar{A})=1-P(A)=\dfrac{2}{3}$$

c)

$$P(\bar{A}\cap \overline{Ch})=P(\bar{A})P(\overline{Ch}|\bar{A})=\dfrac{2}{3}(1-0.215)$$

$$=\dfrac{157}{300}\approx0.5233$$