Q9 - If the winner of a promotional contest is selected

[ohthatpatrick]

Question Type:
Strengthen

Stimulus Breakdown:
Conclusion: This lottery did not meet the fairness requirement.
Evidence: The fairness requirement is that all entrants have an equal chance of winning. In this lottery, 90% of the winners had submitted their entry form during the day 1 or 2 of the 30 day entry period.

Answer Anticipation:
We have to get from "90% of winners entered on day 1 or day 2" to "not all entrants had an equal chance of winning".

Well, why do we think the author is assuming that entrants did NOT all have an equal chance? Why does "90% of the winners came from the first couple days" suggest a bias / tilt in how the winners were picked?

Presumably, the author is thinking, if all days of the 30 period are created equal, then 1/30 of the winners should be from day 1, 1/30 should be from day 2, etc. Since 9/10 of the winners are from day 1 or day 2, it seems to be out of proportion and it looks biased towards the early entries.

But say that 10,000 people entered this lottery as soon as they could (on the first couple days), and then only about 100 people entered the lottery of the next 28 days. Given those numbers, wouldn't we expect 90% (or more) of the winners to be from the first two days? This argument is vulnerable to the objection that "90% of winners coming from the first two days is a totally fair result, if 90% of the lottery entries were submitted during those first two days."

So to strengthen this argument, we want to know that that was NOT the case. We'd want to know that entries came in fairly regularly, or that more entries were submitted near the deadline (near day 30) or near the midpoint (day 15) than were submitted near the opening (near day 1 or 2).

Correct Answer:
C

Answer Choice Analysis:
(A) We don't care about family members, just the proportion of when entries were submitted. But if anything, this makes it sound like the lottery WAS fair.

(B) We don't care whether the matter was publicized or not, just whether it was fair.

(C) YES, this shuts down the objection we considered. If the entry forms were submitted at a consistent rate, then every day should only account for about 1/30 of the winners. Since day 1 and 2 account for 9/10 of the winners, it doesn't seem like every one had an equal chance of winning.

(D) This sounds more like it WAS fair, but also we don't care about whether the rules were posted or not.

(E) The number of people doesn't matter; what matters is the number of day 1 / day 2 vs. the number of entrants on the other 28 days.

Takeaway/Pattern: This is one of those Strengthen questions that is best answered by initially considering how we would OBJECT to the argument. Once we find its vulnerability, we look for an answer that removes that concern.

#officialexplanation

[NanaN402]

Hi there,

Thank you for the explanation. I am still having trouble with this question. When I look at this question and notice our task is to strengthen the argument, I identified the conclusion of the argument to be that the lottery DID NOT meet the fairness requirement, so if we want to strengthen this my thinking is that we are looking for the answer choice that is in support of this and alludes to the lottery NOT being fair. I am confused then how answer choice C is correct since it suggests reasoning that would seemingly make for a fair lottery. If forms were submitted consistently, there should be no question as to the lottery being UNFAIR.

What am I missing here? Please help

[Laura Damone]

Hi there!

First off, good job correctly IDing the question type and conclusion, and prephrasing what the correct answer should do: it should support the claim that this lotto was unfair.

Consider the existing evidence for this position: 90% of the winners entered in the first 2 days. That sure does make it sound like the thing was rigged in favor of early submissions! But this is an Assumption question, so we need to try to spot a gap in this reasoning. I don't see any major term shifts, so I'll think about possible objections. What if almost everybody entered in the first 2 days, too? If that's the case, then it only makes sense that most of the winners would have submitted in the first 2 days.

Answer choice C defends against this objection, telling us that "nope, most of the entries were NOT submitted in the first 2 days." If the submissions were consistent throughout the month, we'd expect the winners to be drawn from submissions throughout the month as well. This makes the fact that winners were drawn mostly from day 1 and 2 all the more suspicious, thereby strengthening the argument that the lotto wasn't fair.

Hope this helps!