Question

In a class of students, the following data table summarizes how many students passed a test and complete the homework due the day of the test. What is the probability that a student chosen randomly from the class passed the test and completed the homework?
Passed the test Failed the test
Completed the homework 9 2
Did not complete the homework 3 5
Answer
Attempt 1 out of 2

Answer 1

To find the probability that a randomly chosen student passed the test and completed the homework, we can use the data from the table you provided.

Here’s the table summarized:

| | Passed the test | Failed the test | Total |
|------------------------|----------------|------------------|-------|
| Completed the homework | 9 | 2 | 11 |
| Did not complete the homework | 3 | 5 | 8 |
| **Total** | **12** | **7** | **19**|

1. **Total number of students** = 19
2. **Number of students who passed the test and completed the homework** = 9

To calculate the probability:

\[
P(\text{Passed and Completed}) = \frac{\text{Number of students who passed and completed}}{\text{Total number of students}} = \frac{9}{19}
\]

Thus, the probability that a randomly chosen student passed the test and completed the homework is \(\frac{9}{19}\).