Question

A recent test can determine with 92% accuracy if a student will pass an online math FINAL by measuring the amount of studying done during the week of the test. Let us say that 5,000 students are chosen at random to participate in the survey. If the test shows a positive, the student passed the FINAL. For this survey, approximately 85% of student actually passed their online math FINAL. Complete the table below for this survey.

	Positive Result	Negative Result	Total
Passed the FINAL
Failed the FINAL
Total			5,000

1. Out of all the people that passed, what are the chances the test was correct and gave the student a positive result?
2. If the student had a negative result, what are the chances they actually passed?

Answer 1

Probability of Accuracy = 92%

No. of Students Appeared is 5000 Students

Passed the Final is = 5000 X 85% = 4250 Students

Failed the Final is = 5000 X ( 100% - 85%) = 750 Students

4250 Student + 750 Student = 5000 Students

Secondly, AS stated 92% probability is the result accuracy,  Hence out of 85% passing percentage only 92% of the same is passed with accuracy. It means 5000 X 85% X 92% = 3910 Students are actually passed.

Third, AS stated 92% probability is the result accuracy, Hence Out of 15% negative result i.e. 750 Students so their result accuracy is 92% it means 5000X 15%X 92% = 690 Students will fail with 92% accuracy hence 750 - 690 = 60 Students , Student will pass on the basis of 8% non accurate data. As per the requirement no. of student will pass from the negative result.