Question

probability from a two - way table
question
for a certain class, the following data table compares how many students passed a test and whether or not they completed the homework due the day of the test. what is the probability that a student chosen randomly from the class failed the test?

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

answer attempt 1 out of 2
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Explanation:

Step1: Find total number of students

First, we sum up all the values in the table. The number of students who passed and completed homework is 13, passed and did not complete is 3, failed and completed is 6, failed and did not complete is 4. So total students = \(13 + 3 + 6 + 4 = 26\).

Step2: Find number of students who failed the test

The number of students who failed the test is the sum of those who failed and completed homework and those who failed and did not complete homework. So that's \(6 + 4 = 10\).

Step3: Calculate the probability

Probability is the number of favorable outcomes (failed the test) divided by total number of outcomes (total students). So probability = \(\frac{10}{26}=\frac{5}{13}\approx0.3846\) (or we can keep it as a fraction \(\frac{5}{13}\) or a decimal). Wait, wait, wait. Wait, the question is "the probability that a student chosen randomly from the class failed the test"? Wait, let's re - check the table. Wait, the two - way table:

Rows: Passed the test, Failed the test.

Columns: Completed the homework, Did not complete the homework.

So for failed the test: completed homework is 6, did not complete is 4. So total failed = \(6 + 4 = 10\). Total students: \(13+3 + 6+4=26\). So probability of failing the test is \(\frac{10}{26}=\frac{5}{13}\).

Wait, maybe I misread the question. Let me check again. The question: "What is the probability that a student chosen randomly from the class failed the test?"

Yes, so total students: \(13 + 3+6 + 4=26\). Number of students who failed: \(6 + 4 = 10\). So probability is \(\frac{10}{26}=\frac{5}{13}\approx0.385\) or \(\frac{5}{13}\).

Wait, but let's confirm the table values:

• Passed the test:
• Completed homework: 13
• Did not complete: 3
• Failed the test:
• Completed homework: 6
• Did not complete: 4

Total students: \(13 + 3+6 + 4=26\).

Number of students who failed the test: \(6 + 4 = 10\).

So probability \(P(\text{failed the test})=\frac{\text{Number of students who failed}}{\text{Total number of students}}=\frac{10}{26}=\frac{5}{13}\).

Answer:

\(\frac{5}{13}\) (or approximately \(0.385\))