Math  /  Data & Statistics

QuestionProbability from a Two Way Table Score: 0/5 Penalty: 1 off
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In a class of students, the following data table summarizes how many students passed a test a complete the homework due the day of the test. What is the probability that a student chosen randomly from the class passed the test or completed the homework? \begin{tabular}{|c|c|c|} \hline & Passed the test & Failed the test \\ \hline Completed the homework & 17 & 2 \\ \hline Did not complete the homework & 3 & 4 \\ \hline \end{tabular}
Answer Attempt 2 out of 2 0.846 \square Submit Answer

Studdy Solution

STEP 1

What is this asking? What's the chance a random student from this class either passed *or* did their homework, or *both*? Watch out! Don't just add the totals for passing and for homework!
Some students did *both*, and we don't want to count them twice!

STEP 2

1. Total Students
2. Students Who Passed *or* Did Homework
3. Calculate Probability

STEP 3

Let's **find the total number of students** in the class.
This is like finding the total number of slices in a giant pizza before figuring out how many slices *you* get!
We add up *all* the numbers in the table!

STEP 4

17+2+3+4=2617 + 2 + 3 + 4 = 26 There are **26** total students.
This is our "whole pizza"!

STEP 5

Now, let's find how many students either passed the test *or* completed the homework.
This is like figuring out how many slices of pizza have your *favorite* toppings!

STEP 6

1717 students both passed and did homework. 22 students did homework but didn't pass. 33 students passed but didn't do homework. 44 students neither passed nor did their homework.

STEP 7

We want the number of students who passed *or* did homework.
That's 17+2+3=2217 + 2 + 3 = 22.
Remember, the 1717 students already cover both passing *and* doing homework, so we don't count them twice!

STEP 8

Probability is just the number of "successful" outcomes (students who passed or did homework) divided by the total number of possible outcomes (all students).
It's like figuring out what fraction of the pizza has your favorite toppings!

STEP 9

We have **22** students who passed or did homework (our "favorite toppings") and **26** total students (the "whole pizza").

STEP 10

So, the probability is: 2226=11130.846\frac{22}{26} = \frac{11}{13} \approx 0.846

STEP 11

The probability that a randomly chosen student passed the test *or* completed the homework is approximately 0.846\mathbf{0.846}.

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