"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."

Verified step by step guidance

1. Step 1: Understand the problem. We are tasked with finding the probability that a student passed the NCLEX-RN exam, given that the student repeated the exam. This is a conditional probability problem, where we need to focus on the 'Repeat' row of the table.
2. Step 2: Recall the formula for conditional probability. The probability of event A given event B is calculated as P(A|B) = P(A ∩ B) / P(B). In this case, A is 'Passed' and B is 'Repeated the exam'.
3. Step 3: Identify the relevant values from the table. From the 'Repeat' row, the number of students who passed is 44,983, and the total number of students who repeated the exam is 104,758.
4. Step 4: Apply the formula. The conditional probability P(Passed | Repeated) is calculated as the number of students who passed and repeated (44,983) divided by the total number of students who repeated the exam (104,758).
5. Step 5: Simplify the fraction or calculate the division to find the probability. This step involves performing the division 44,983 / 104,758 to get the final probability value.

Key Concepts

Conditional Probability

Conditional probability refers to the likelihood of an event occurring given that another event has already occurred. In this context, it involves calculating the probability that a nursing student passed the NCLEX-RN exam, given that they are a repeat test-taker. This is expressed mathematically as P(Pass | Repeat), which requires using the number of repeat students who passed divided by the total number of repeat students.

Total Probability

Total probability is a fundamental concept in probability theory that helps in calculating the overall likelihood of an event by considering all possible scenarios. In this case, it involves understanding the total number of students who took the exam, both first-time and repeat test-takers, to contextualize the passing rates. This concept is essential for determining the base rates needed for calculating conditional probabilities.

Data Interpretation

Data interpretation involves analyzing and making sense of numerical data presented in tables or charts. In this question, it requires extracting relevant figures from the provided table, such as the number of repeat students who passed and the total number of repeat students, to compute the desired probability. Effective data interpretation is crucial for accurately answering statistical questions and drawing valid conclusions.