Question

The probability that a randomly selected person has high blood pressure (the event H) is P(H) = 0.4 and the probability that a randomly selected person is a runner (the event R) is P(R) = 0.4. The probability that a randomly selected person has high blood pressure and is a runner is 0.1. Find the probability that a randomly selected person either has high blood pressure or is a runner or both.

Answer 1

0.7 is the probability that a randomly selected person either has high blood pressure or is a runner or both.

Explanation:

We are given the following information in the question:

Probability that a randomly selected person has high blood pressure = 0.4

`P(H) = 0.4`

Probability that a randomly selected person is a runner = 0.4

`P(R) = 0.4`

Probability that a randomly selected person has high blood pressure and is a runner = 0.1

`P(H \cap R) = 0.1`

If the events of selecting a person with high blood pressure and person who is a runner are independent then we can write:

`P(H \cup R) = P(H) + P(R)-P(H\cap R)`

Probability that a randomly selected person either has high blood pressure or is a runner or both =

`P(H \cup R) = P(H) + P(R)-P(H\cap R)\\P(H \cup R) = 0.4 + 0.4 -0.1 = 0.7`

0.7 is the probability that a randomly selected person either has high blood pressure or is a runner or both.