Logical Reasoning

PT152 · S2 · Q9 If the winner of a promotional

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If the winner of a promotional contest is selected by a lottery, the lottery must be fair, giving all entrants an equal chance of winning.

Conclusion

The lottery did not meet the fairness requirement.

Evidence

The fairness requirement is that all entrants have an equal chance of winning.

90% of the winners selected by this lottery submitted their entry forms within the first 2 days of the 30 day registration.

Evaluate

Let's say there were 100 winners to this contest. If every day was equally likely to have contest winners, then there would be 3.3 winners per day for the 30 days the registration period was open.

Our author is picturing this math in her head, and saying if 90% of winners came from the first 2 days, it seems like every day wasn't equally likely to have a contest winner.

Of course the actual fairness rule is that . So why is it that the author thinks some entrants had a bigger / smaller chance?

She's assuming that there were a comparable number of entrants on each of the 30 days. If that were the case, then the people who submitted sometime between day 3 and day 30 would be like,

But if most people got their entries in right when the registration period opened, then we would expect a bigger percentage of winners to have come from that time period.

Pretend we have 1000 entrants over a 10 day period, 100 entries per day. 100, 100, 100, 100, 100, 100, 100, 100, 100, 100

If 90 of the 100 winners came from the first two days, that would seem fishy and unfair.

But suppose most of the entries came in the beginning of the 10 day period. 500, 400, 20, 15, 15, 10, 10, 10, 10, 10

Now, wouldn't we expect most of the contest winners to be people who submitted during the first two days? After all, 90% of the entries came in the first two days, so we'd expect 90% of the randomly drawn winners to come from the first two days.

Goal

Since this argument is vulnerable to one big mathematical objection (what if 90% of the entries were submitted in the first two days?), we should probably expect an answer that rules out that idea.

9.

Which one of the following, if true, most strengthens the argument?

  1. The family members of the

    Weakens, if anything

    This is very weak and tangential, but if anything it would weaken the idea that this was an unfair lottery.

    1% picked this

  2. The manner in which the

    No Impact

    This is so bland and generic that it doesn't change the conversation at all. If anything, the fact that the contest was transparent about how they would select the winner would make it seem more like a fair lottery.

    10% picked this

  3. Correct

    The contest entry forms were

    Why this is right

    This rules out the big objection we had -- "what if 90% of the entries came in the first two days?"

    Skill tested: Strengthen · how this choice captures the argument's function is the move to repeat next time.

    74% picked this

  4. The rules of the contest

    No Impact

    This is just like (B). The fact that the contest was transparent about the rules and the winner-selection process doesn't help us evaluate the author's case at all. The author is just claiming that the lottery didn't meet the fairness requirement -- its winner-selection process might violate the fairness requirement, even if the contest was transparent about the rules and the selection process.

    12% picked this

  5. The number of people entering

    No Impact

    Having a higher or lower than expected total number of contestants doesn't matter. We only care about whether 90% or way less than 90% of the entries were received in the first 2 days of the registration period.

    4% picked this

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