PLEASE help with statistical probability questions!

Question

In a math class with 19 students, a test was given the same day that an assignment was due. There were 11 students who passed the test and 14 students who completed the assignment. There were 3 students who failed the test and also did not complete the assignment. What is the probability that a student chosen randomly from the class completed the homework?

Answer 1

14/19 = about 73.68%

= number who did the assignment over total number of students = 14/19 chance

whoever designed this question is trying to trick you into thinking you have to use the other information given in the problem. It's all a distraction

Answer 2

What I like do in this type of problem is first fill in a Venn Diagram.

So imagine a Venn diagram with 2 overlapping circles labeled T (representing the set of students who passed the test) and A (representing the set of students who completed the assignment).

Now put a 3 outside both circles representing the students who both failed the test and did not complete the assignment.

That means the total in the 2 circles must be 19 - 3 = 16.

So the overlap will be 11 + 14 - 16 = 9 (representing the students who both passed the test and completed the assignment).

So 11 - 9 = 2 students who passed the test but did not complete the assignment.

And 14 - 9 = 5 students who completed the assignment but did not pass the test.

The probability of a student chosen randomly completing the assignment is 14/19 = .74 rounded.

Answer 3

I wonder if I'm reading the problem wrong, because it seems that a lot of the provided information is irrelevant. 14 of the 19 students completed the assignment, so the probability that a randomly chosen student completed the assignment should just be 14/19.