Question

you only have 3 questions left to raise your score.
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?

	completed the homework	did not complete the homework
failed the test	4	6

answer attempt 1 out of 2

Explanation:

Step1: Identify relevant counts

We need the number of students who passed the test and completed the homework (9) and the number of students who completed the homework (9 + 2 = 11).

Step2: Apply conditional probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, this is $\frac{\text{Number of } A\cap B}{\text{Number of } B}$. Here, $A$ is "passed the test" and $B$ is "completed the homework". So we calculate $\frac{9}{9 + 2}=\frac{9}{11}$.

Answer:

$\frac{9}{11}$