In a math class with 28 students, a test was given the same day that an assignment was due. There were 20 students who passed the test and 19 students who completed the assignment. There were 16 students who passed the test and also completed the assignment. What is the probability that a student passed the test given that they completed the homework?
Well, if you were hoping for a straightforward answer, I'm afraid you won't find it here! However, I can still give you a mathematically accurate response laced with a touch of humor.
To calculate the probability that a student passed the test given that they completed the homework, we need to use conditional probability. Shall we proceed?
Okay, let's consider this situation. Out of a class of 28 students, there are 19 diligent souls who completed the assignment. However, we have a bunch of classmates who couldn't be bothered with it. Tsk, tsk!
Now, out of these committed 19 students, 16 of them also managed to ace the test. Well done, smarty-pants! Now, imagine all these students standing in a line. We’re going to use these numbers to do some fancy math (not really).
The probability that a student passed the test given that they completed the homework can be calculated by dividing the number of students who passed both the homework and the test (16) by the total number of students who completed the homework (19).
So, to sum it all up in a not-so-serious way, the probability of passing the test given that the homework is completed is 16 out of 19. Congrats to those 16 students who put in the effort and aced both, and may the rest of the class learn from their shining example!
To calculate the probability that a student passed the test given that they completed the homework, we need to use conditional probability.
Let's define the following events:
A: Student passed the test
B: Student completed the homework
We are given:
P(A) = 20/28 (probability that a student passed the test)
P(B) = 19/28 (probability that a student completed the homework)
P(A ∩ B) = 16/28 (probability that a student passed the test and completed the homework)
The probability that a student passed the test given that they completed the homework can be calculated using the formula:
P(A|B) = P(A ∩ B) / P(B)
Substituting the given values:
P(A|B) = (16/28) / (19/28)
Now let's simplify:
P(A|B) = 16/19
Therefore, the probability that a student passed the test given that they completed the homework is 16/19.
To find the probability that a student passed the test given that they completed the homework, we need to calculate the conditional probability.
The conditional probability can be calculated using the formula:
P(A|B) = P(A ∩ B) / P(B), where A and B are two events.
In this case, event A is passing the test, and event B is completing the assignment.
We are given that there were 16 students who passed the test and also completed the assignment. So, P(A ∩ B) = 16.
We are also given that there were 19 students who completed the assignment. So, P(B) = 19.
Now, we can substitute the values in the formula to find the probability:
P(A|B) = P(A ∩ B) / P(B)
= 16 / 19
Therefore, the probability that a student passed the test given that they completed the homework is 16/19 or approximately 0.842.
draw Venn diagram
passed test ---- both - did assignment
20-16=4 -------- 16 -------- 19-16 = 3
4 + 16 + 3 = 23 who did something useful
that leaves 28 - 23 = 5 outside your diagram who did nothing
16 out of the 19 who did the homework passed the test
so
16/19 = 0.842
Doing the homework seems to have helped them pass the test.