Mariha is evaluating three different driving schools. She asked 50 people who attended one of the schools whether they passed the driving test on the first try. The results of the survey are shown in the table below. P is the probability of randomly selecting a student who passed on the first try from the students who attended A-1 Driving School. Q is the probability of randomly selecting a student who attended A-1 Driving School from the students who passed the driving test on the first try. Which of the following must be true?
P > Q
The probability P represents the likelihood of selecting a student who passed from those who attended A-1 Driving School, while Q represents the likelihood of selecting a student who attended A-1 from those who passed. Due to the nature of conditional probabilities, P is generally greater than Q, especially if the passing rate for A-1 is higher than average.
This statement suggests that the two probabilities are equal, which is unlikely in most cases. P measures the success rate among A-1 students, while Q assesses A-1's share among all successful test-takers. Unless the passing rate for A-1 students is equal to the overall passing rate, this equality will not hold.
Saying that P is less than Q implies that the probability of passing among A-1 students is lower than the overall success rate, which contradicts the assumption that A-1 has a higher success rate. If A-1 students perform better than average, P must be greater than Q.
This statement correctly reflects the relationship between the two probabilities. If A-1 Driving School has a higher than average passing rate, then the probability of selecting a successful A-1 student (P) will indeed be greater than the probability of selecting an A-1 student from the pool of successful candidates (Q).
This statement is incorrect because P and Q are both measurable probabilities derived from the same dataset. They can be compared as they relate to the same events, just viewed from different perspectives.
In evaluating the probabilities P and Q, we find that P is greater than Q under typical circumstances where A-1 Driving School has a favorable passing rate. This relationship highlights the distinction between conditional probabilities, revealing how the context of the sampled groups influences the interpretation of success rates. Thus, understanding these probabilities aids in making informed decisions about the effectiveness of driving schools.
Related Questions
View allIn the xy-plane, line l passes through the points (4, 4) and (9, 6). W...
The repeating decimal 0.111... is equivalent to
A recipe for strawberry jam requires two pounds of berries to make fiv...
If a number is selected at random from the list above, what is the pro...
A cafeteria has created a healthy snack by mixing unsalted cashews and...
Related Quizzes
View allACCUPLACER Next Generation Arithmetic
Next Generation ACCUPLACER Arithmetic Practice Test
ACCUPLACER Next Generation Arithmetic Answers
Next Generation Arithmetic ACCUPLACER
Next-Generation ACCUPLACER Arithmetic
ACCUPLACER Next-Generation Arithmetic Scores
ACCUPLACER Next Generation Quantitative Reasoning Algebra and Statistics
ACCUPLACER Next Generation Quantitative Reasoning Algebra and Statistics Answers
Next Generation ACCUPLACER Scores Quantitative Reasoning Algebra and Statistics
ACCUPLACER Next Generation Quantitative Reasoning Algebra and Statistics Scores
- ✓ 500+ Practice Questions
- ✓ Detailed Explanations
- ✓ Progress Analytics
- ✓ Exam Simulations