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

Way overworked!

14 did homework out of a class of 19 (explicit!)

14 / 19 ≈ 74%

Answer 2

P(passed) = 11/19

P(HW completed) = 14/19

P(failed & not completed) = 3/19

P(HW completed) = ? 14/19?

is there a typo or some other missing information? If 14 completed the assignment and there were 19 students, then probability a randomly chosen student completed the assignment is 14/19 = about 73.7%

all other information seems irrelevant, unless there's something more to the problem than as stated.

Maybe the problem really was to ask what is the probability that a randomly selected student completed the assignment and passed the test? That's 9/19 = about 47.4%. Draw a Venn diagram

9 is the overlap between passing & completing the assignment

11 passed

14 completed the assignment

9 passed & completed the assignment

2 passed but did not complete the assignment

5 failed but did complete the assignment

3 failed and did not complete the assignment

5 failed but did not complete the assignment

2 passed but did not complete the assignment

draw a rectangle that contains 19 students total

draw 2 circles, one for those who passed

another overlapping circle for those who completed the assignment

outside the 2 circles are 3 students

inside the 2 circles are 19-3 = 16 students

the overlap is 9 students