What is the probability that a student completed the homework given that they passed the test? Passed the test Failed the test Completed the homework 12 3 Did not complete the homework 2 6
To find the probability that a student completed the homework given that they passed the test, we need to use the formula for conditional probability:
P(A|B) = P(A and B) / P(B)
In this case, event A is completing the homework and event B is passing the test.
P(A and B) = Number of students who completed the homework and passed the test = 12
P(B) = Number of students who passed the test = 12 + 3 = 15
Therefore, the probability that a student completed the homework given that they passed the test is:
P(A|B) = 12 / 15 = 0.8
So, the probability is 0.8 or 80%.