Question

n a group of 40 people, 10 people are healthy. The 30 unhealthy people have either high blood pressure, high cholesterol, or both. Suppose 15 have high blood pressure and 25 have high cholesterol. If a person is randomly selected from this group, what is the probability that they have both high blood pressure and high cholesterol

Answer 1

If a person is randomly selected from this group, the probability that they have both high blood pressure and high cholesterol is P=0.25.

Explanation:

We can calculate the number of people from the sample that has both high blood pressure (HBP) and high cholesterol (HC) using this identity:

`N(\text{HBP or HC})=N(\text{HBP})+N(\text{HC})-N(\text{HBP and HC})\\\\\\ N(\text{HBP and HC})=N(\text{HBP})+N(\text{HC})-N(\text{HBP or HC})\\\\\\ N(\text{HBP and HC})=15+25-30=10`

We can calculate the probability that a random person has both high blood pressure and high cholesterol as:

`P(\text{HBP and HC})=(10)/(40)=0.25`