Question

in a class of students, the following data table summarizes how many students passed a test and completed the homework due the day of the test. what is the probability that a student passed the test given that they completed the homework?

	passed the test	failed the test
did not complete the homework	3	6

Explanation:

Step1: Identify relevant counts

Students who completed homework: $19 + 2 = 21$; passed among them: $19$

Step2: Calculate conditional probability

Probability = $\frac{\text{Passed and completed homework}}{\text{Completed homework}} = \frac{19}{21}$

Answer:

$\frac{19}{21}$