Question

In a math class with 18 students, a test was given the same day that an assignment was due. There were 11 students who passed the test and 10 students who completed the assignment. There were 5 students who failed the test and also did not complete the assignment. What is the probability that a student failed the test given that they completed the homework?
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Answer 1

4/29 is the probability that a student who did not complete the homework passed the test.

Step-by-step explanation:

It is given that,

There are 29 students in a math class.

Two types of students who passed the test and are not passed the test.

The other two types of students are who completed the assignment and did not complete the assignment.

So, the given data can be formed as a table.

There were 22 students who passed the test.

There were 20 students who completed the assignment.

There were 18 students who passed the test and also completed the assignment.

                                        Passed the test     Not passed the test    Total

Completed assignment        18                             -                             20

Not completed assignment   x                             -                                -

Total                                       22                           -                               29

Now, you need to find the probability that a student who did not complete the homework passed the test.

⇒ No.of students completed assignment passed the test / Total students.

To find the no.of students completed assignment passed the test :

Let 'x' is the no.of students completed assignment passed the test.

⇒ 18+x = 22

⇒ x = 22 - 18

⇒ x = 4

∴ P(students completed assignment passed the test) = 4 / 29.