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
= [tex]\frac{18}{27}[/tex]
P(2) = Probability of those that completed homework
= 15+2 = 17
= [tex]\frac{17}{27}[/tex]
P(1 U 2) = student that passed and did completed homework/total
= [tex]\frac{15}{27}[/tex]
Probability that a student chosen randomly from the class did not complete the homework
= [tex]\frac{18}{27} +\frac{17}{27} -\frac{15}{27}[/tex]
= 0.6667+0.6296-0.5556
= 0.7407
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