Question

1. the probability that a randomly selected person has high blood pressure (the event h) is p(h) = 0.2 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. a) .4 b) .5 c) .6 d) .8 e) .9 f) none of the above

Explanation:

Step1: Recall the addition rule for probability

The formula for the probability of the union of two events \( H \) and \( R \) is \( P(H \cup R) = P(H) + P(R) - P(H \cap R) \).
Given \( P(H) = 0.2 \), \( P(R) = 0.4 \), and \( P(H \cap R) = 0.1 \).

Step2: Substitute the values into the formula

Substitute the given probabilities into the formula:
\( P(H \cup R) = 0.2 + 0.4 - 0.1 \)

Step3: Calculate the result

First, add \( 0.2 \) and \( 0.4 \): \( 0.2 + 0.4 = 0.6 \).
Then, subtract \( 0.1 \) from \( 0.6 \): \( 0.6 - 0.1 = 0.5 \).

Answer:

B) .5