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 did not complete the homework? Passed the test Failed the test Completed the homework 13 6 Did not complete the homework 3 4

Answer 1

Complete 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 or completed the homework?

Passed the test Failed the test Total

Completed the homework 15 2 17

Did not complete the homework 3 7 10

Total 18 9 27

The probability that a person chosen randomly from the class did not complete the homework is 0.7407

The total number of people in this class = 27

Total number of people that passed = 15 + 3 = 18

We have two events

• Event 1: A random student passed the test
• Event 2: A random student completed the homework

We are to find probability of event 1 or 2

= P(1) +P(2) - P(1 U 2)

P(1) = Probability of those that passed

= $\frac{18}{27}$

P(2) = Probability of those that completed homework

= 15+2 = 17

= $\frac{17}{27}$

P(1 U 2) = student that passed and did completed homework/total

= $\frac{15}{27}$

Probability that a student chosen randomly from the class did not complete the homework

= $\frac{18}{27} +\frac{17}{27} -\frac{15}{27}$

= 0.6667+0.6296-0.5556

= 0.7407

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