The probability that a randomly selected person has high blood pressure (the event H) is P(H) = 0.3 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 is a runner, given that he has high blood pressure

To find the probability that a randomly selected person is a runner given that they have high blood pressure, we need to use **conditional probability**. The formula for conditional probability is:

\[
P(R | H) = \frac{P(R \cap H)}{P(H)}
\]

Where:
- \(P(R | H)\) is the probability that the person is a runner given they have high blood pressure.
- \(P(R \cap H)\) is the probability that the person is both a runner and has high blood pressure (which is given as 0.1).
- \(P(H)\) is the probability that the person has high blood pressure (given as 0.3).

Now we can substitute the values into the formula:

\[
P(R | H) = \frac{0.1}{0.3} = \frac{1}{3} \approx 0.3333
\]

So, the probability that a randomly selected person is a runner given that they have high blood pressure is approximately **0.3333** (or 33.33%).

Would you like further details or explanations?

### Related Questions:
1. What is the probability that a person is neither a runner nor has high blood pressure?
2. How do we calculate the probability that a person has high blood pressure but is not a runner?
3. If the events were independent, how would the joint probability \( P(R \cap H) \) change?
4. What is the probability that a person either has high blood pressure or is a runner?
5. Can we use Bayes' Theorem to verify the result? How?

### Tip:
Always ensure you understand the difference between **conditional** and **joint** probabilities, as they serve distinct purposes in probability theory.

The probability that a randomly selected person has high blood pressure (the event H) is P(H) = 0.3 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 is a runner, given that he has high blood pressure.

Discover how to calculate the probability that a person is a runner, given that they have high blood pressure, using the conditional probability formula. Learn key concepts such as joint probability and conditional probability. This problem involves basic probability theory, ideal for Grades 10-12.

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