In a class of students, the following data table summarizes how many students passed a test and completed the homework due the day of the test. What is the probability that a student passed the test given that they did not complete the homework?Passed the test Failed the testCompleted the homework 9 3Did not complete the homework 4 6
Question
In a class of students, the following data table summarizes how many students passed a test and completed the homework due the day of the test. What is the probability that a student passed the test given that they did not complete the homework?Passed the test Failed the testCompleted the homework 9 3Did not complete the homework 4 6
Solution
To find the probability that a student passed the test given that they did not complete the homework, we need to use the formula for conditional probability:
P(A|B) = P(A ∩ B) / P(B)
Where:
- A is the event that a student passed the test
- B is the event that a student did not complete the homework
- P(A ∩ B) is the probability of both A and B occurring
- P(B) is the probability of B occurring
From the data table, we can see that:
- 4 students passed the test and did not complete the homework (A ∩ B)
- 10 students did not complete the homework (B)
So, we can substitute these values into the formula:
P(A|B) = P(A ∩ B) / P(B) = 4 / 10 = 0.4
Therefore, the probability that a student passed the test given that they did not complete the homework is 0.4 or 40%.
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