AP Stats Unit 4 Practice FRQ #2

The FRQ Unit 4 Exam Practice Prompt

FRQ Writing Samples & Feedback

Sample Response 1

Your responses in part (a) and (b) are clear, concise, and demonstrate understanding of the topic at hand (“the probability of success is not constant”) is the key in part (a). In part ( c ), however, you mention that each trial of the simulation would have the same probability of success… which is the exact opposite of what you mentioned in part (a). So the simulation would not do what the debate coach proposed, since the simulation would have independent trials; the debate coach did not. [An extension: the simulation would simulate getting P(x = 4) as a binomial random variable] Therefore you would not earn credit for part ( c ).

Sample Response 2

In part (a), you give the correct reasoning (the trials are not independent), and explain what that represents… in general. That is, your answer is not presented in the context of the scenario. To ensure you get the “context” component, name the variable involved or describe what is being measured in some way. In this example, instead of “the outcome of a trial can have an effect on the other trials”, you could say “the outcome of the first student being picked impacts the results of the other selections” or “the probability of drawing a lowerclassmen would be dependent on the previous selections” or something to that effect.

Your work in part (b) is correct, with correct calculations and work shown. Full credit there.

In part ( c ), you do a good job of defending your answer of “no” - explaining why the proposed simulation results in independent trials, whereas the selection process originally proposed does not. This is the correct explanation. Nice job!

Sample Response 3

I’m going to take a stab at explaining “independent” in this context in writing: for trials to be “independent,” the probability of a successful trial (in this case, picking a lowerclassman) must remain constant from one trial to the next (as you mention). So, as you say, the scenario does not lend itself to independent trials, and binomial calculations do not apply. However, when you say “the probability … decreases to only 4 rather than 5”, we should be careful: probability can’t be whole numbers like that (only proportions between 0 and 1), so that is a misuse of the word (we could say 4/14 rather than 5/15 and be OK though). Please let me know if the above doesn’t address your question.

Your answer to part (b) is spot on - work shown and everything. For part ( c ) , you correctly answer “no” while citing the idea that one person could be picked twice. I think you can strengthen your answer by making it clear that that cannot happen when we sample without replacement (instead of the more vague “that does not make sense”). You should still land somewhere near full credit with the response, though.

Sample Response 4

Good responses! You do a good job of being concise, while still saying everything needed to demonstrate understanding. In part ( c ), you could do a little more to demonstrate that the simulation results in independent trials (you describe this without explicitly naming it), which is why the design is not an accurate model.

Sample Response 5

Nicely done! All three parts are thorough and contain correct information!

Sample Response 6

Nice job! One thing to point out: in part ( c ), you defend your answer by mentioning “the probability of choosing an upperclassmen or underclassmen changes each time” - that provides context in your response. Your answer in part (a), while correct, does not have that same level of context (you just say “does not meet the condition of having the same probability of success for each trial”, which is a generic answer and not in-context for this problem). Be sure to include context wherever possible in your answers.

Sample Response 7

Well done! This looks like a case of all three answers correct with appropriate supporting work/details.

Sample Response 8

Very good description on part (a)! You give your explanation for the trials not be independent in context of the situation. For part (b), you’ve correctly calculated the probability with appropriate supporting work, and in part ( c ) you make it clear that the proposed simulation has independent trials (you don’t say the word independent, but your description is clear enough that it is understood). Nice job!

Sample Response 9

Nice job! You’ve given clear explanations/calculations in all three parts, and all are correct.

Sample Response 10

Solid work. On part (a), you’ll need to do more to explain why X is not independent - the reason is because we’re drawn without replacement, but you’ll need to explain a little more like you did in part (b) or part ( c ) about the probability changing for each trial.

Sample Response 11

Solid work throughout here. Be careful in part (a) - you’re giving the correct answer (no), with the correct reason (the selection without replacement makes the trials dependent), but your description of “the probability of each student being select goes up after every index card” is missing the fact that this is assuming those students didn’t already get picked, which you don’t explicitly mention. It could lead to a false conclusion (once a certain student is picked, the probability they get picked again is not 0, and hence went down). You could edit your statement to say “every time a student is not picked, the probability of them being selected goes up”… hence the trials are dependent. In (b) and ( c ) you do everything correctly.