Question

In a math class with 21 students, a test was given the same day that an assignment was due. There were 12 students who passed the test and 13 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 who passed the test completed the homework?

Answer 1

9/12 OR 3/4

Step-by-step explanation:

Answer 2

Answer:12/17

Explanation:Using the formula for conditional probability, we have:

P(B|A) = P(A and B) / P(A)

We can find P(A and B) by noticing that there are 12 students who passed the test and completed the assignment. Therefore:

P(A and B) = 12/21

To find P(A), we need to consider all the students who passed the test, regardless of whether they completed the assignment or not. This includes the 12 students who passed the test and completed the assignment, as well as the 5 students who failed the assignment but did not complete it. Therefore:

P(A) = (12 + 5)/21

Now we can plug these values into the formula for conditional probability:

P(B|A) = (12/21) / ((12 + 5)/21)

Simplifying this expression, we get:

P(B|A) = 12/17

Therefore, the probability that a student who passed the test completed the homework is 12/17.