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?

Explanation:

Step1: Calculate total number of students

Add all values in the table: \(13 + 6+3 + 4\).
\(13+6 + 3+4=(13 + 6)+(3 + 4)=19 + 7=26\)

Step2: Calculate number of students who failed the test

Add the values in the "Failed the test" column: \(6+4\).
\(6 + 4=10\)

Step3: Calculate the probability

Probability formula is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, number of favorable outcomes (failed) is \(10\), total number of outcomes is \(26\). So \(P=\frac{10}{26}\). Simplify the fraction: \(\frac{10\div2}{26\div2}=\frac{5}{13}\)

Answer:

\(\frac{5}{13}\)