Question

relative frequencies and association
students and teachers at a school were asked whether they can run a half - marathon. the conditional relative frequencies by row of the raw data are recorded in the table.
juan is a student. what is the probability he cannot run a half - marathon?
enter your answer in the box.

Explanation:

Step1: Use the row total property

In the row for students, the sum of the conditional - relative frequencies (for "Yes" and "No") is equal to 1. Let \(P(\text{Yes})\) be the probability that a student can run a half - marathon and \(P(\text{No})\) be the probability that a student cannot run a half - marathon. We know that \(P(\text{Yes})+P(\text{No}) = 1\).

Step2: Solve for \(P(\text{No})\)

Given \(P(\text{Yes})=0.1\). Substitute into the equation \(P(\text{Yes})+P(\text{No}) = 1\). Then \(P(\text{No})=1 - P(\text{Yes})\).

$$P(\text{No})=1 - 0.1=0.9$$

Answer:

\(90\)