"In Exercises 17 and 18, use the table, which shows the number...

Question

"In Exercises 17 and 18, use the table, which shows the numbers of first-time and repeat U.S. nursing students taking the National Council Licensure Examination (NCLEX-RN® exam) to pass or fail in a recent year. (Adapted from National Council Licensure Examinations)

18. Find the probability that a student passed, given that the student repeated the exam."

18. Find the probability that a student passed, given that the student repeated the exam."

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A university records the number of first time and returning students who passed or failed a final exam. The data is as follows. Passed, failed, first time students, 12,500, 2300, returning students, 3800, 2200. What is the probability that a student passed given that the student was returning? Awesome. So it appears for this particular problem we're asked to determine what is the probability that a student passed the final exam given that the student was a returning student. So now that we know what we're trying to solve for, let's read off our multiple choice answers to see what our final answer might be. A is 0.633, B is 0.534, C is 0.619, and D is 0.456. Awesome. Our first step that we need to take is we need to note that the number of returning students who passed, which you'll call RP, so this is returning students who passed, is equal to 3800. Our second step now is we need to determine the total number of returning students, so we need to take 3800 plus 2200, which is equal to 6000. Our third step now is we need to determine the probability P. So the probability P of past bar returning, which I'll just call R, is equal to 3800 divided by 6000. Which when we perform this calculation, we will find when we round to three decimal places that will be approximately equal to 0.633, and that is our final answer. Hooray, we did it. So therefore, without a doubt, the probability that a student passed the the given final exam and that the student was returning is 0.633. Or we can also say that this is 63.3% if we if we convert our decimal to a percentage, but we can leave our answer as a decimal because all of our multiple choice answers are written as decimals. So that means without a doubt, our final answer has to be multiple choice answer letter A, which once again is 0.633. And that's it. That is our final answer. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

Key Concepts

Conditional Probability

Total Probability

Data Interpretation

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