HardStatistics & Data ScienceHigh School (9–10)High School (11–12)UndergraduateGeneralStatistics Basics › Probability and ChanceStatistics Basics › Tables and GraphsNumericalConceptual
Two made-up classes sit the same test. Class A has 30 students, and 24 of them pass…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Two made-up classes sit the same test. Class A has students, and of them pass. Class B has students, and of them pass. Make the two-way table of class against result. Find the probability of a pass, given class A, and given class B. Then a student who failed is picked at random. Find the probability that the student is from class A. Give four decimal places.
Need a reminder? The key ideaShow
In a two-way table, is the count of and divided by the count of : look only at the row or column of . In shares, .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The table. Class A: pass, fail. Class B: pass, fail. In all pass and fail, out of students.
Step 2. Pass given class. Class A: . Class B: .
Step 3. Class A given fail. .
Answer: , and about .
Watch out. Class A did better, and class A is bigger. Even so, fewer than half of the students who failed are from class A. Turning a conditional probability around always needs the whole table.
Discussion (0)
Log in to join the discussion.
Loading…