In a class of students, the following data table summarizes how many students passed a test and complete the homework due the day of the test. What is the probability that a student who passed the test completed the homework?
Passed the test Failed the test
Completed the homework 19. 2
Did not complete the homework 3 6
There are a total of 19 + 2 + 3 + 6 = 30 students in the class. Out of the 19 students who passed the test, 19-3 = 16 completed the homework. So the probability that a student who passed the test completed the homework is 16/19.
In a class of students, the following data table summarizes how many students passed a test and complete the homework due the day of the test. What is the probability that a student completed the homework given that they failed the test?
Passed the test Failed the test
Completed the homework 8 3
Did not complete the homework 2 5
Out of the students who failed the test, a total of 3 + 5 = 8 did not complete the homework. So the probability that a student did not complete the homework given that they failed the test is 8/8 = 1.
Therefore, the probability that a student completed the homework given that they failed the test is 0 (because all students who failed the test did not complete the homework).
To calculate the probability that a student who passed the test completed the homework, we need to use the concept of conditional probability. Conditional probability is the likelihood of an event occurring given that another event has already occurred.
In this case, the event "A student completed the homework" is contingent on the event "A student passed the test." The probability of A given B is denoted as P(A|B). So, we want to find P(completed homework | passed the test).
The formula for conditional probability is:
P(A|B) = P(A and B) / P(B)
In this case, P(A and B) represents the number of students who both passed the test and completed the homework, which is 19. And P(B) represents the number of students who passed the test, which is 19 + 3 = 22.
So, the probability that a student who passed the test completed the homework is:
P(completed homework | passed the test) = 19 / 22 ≈ 0.86 or 86%
To find the probability that a student who passed the test completed the homework, we need to calculate the ratio of the number of students who passed the test and completed the homework to the total number of students who passed the test.
Step 1: Add up the number of students who passed the test and completed the homework: 19.
Step 2: Add up the number of students who passed the test: 19 + 2 = 21.
Step 3: Divide the number of students who passed the test and completed the homework by the total number of students who passed the test: 19 / 21.
Step 4: Calculate the probability: 19 / 21 ≈ 0.9048.
Therefore, the probability that a student who passed the test completed the homework is approximately 0.9048, or 90.48%.