PrepTest 106, Section 1, Question 3
For any given ticket in a 1000-ticket lottery,(21 more words not shown)
Which one of the following(13 more words not shown)
- AIt is reasonable(28 more words not shown)
- BWhen the chances(37 more words not shown)
- CIt is unreasonable(21 more words not shown)
- DIt is reasonable(52 more words not shown)
- EFor any given(29 more words not shown)
Reading the argument
One ticket will probably lose. That doesn't mean every ticket will lose.
Imagine a lottery with 1,000 tickets and exactly one winner. Pick any particular ticket beforehand: it has only one chance in 1,000. Predicting that this particular ticket will lose makes sense. Yet somebody has the winning ticket. The very same setup makes each individual ticket unlikely to win while guaranteeing a winner somewhere in the collection.
What we’re looking for
The author takes a reasonable prediction about any one ticket and stretches it into a prediction that there will be no exceptions across all the tickets. Those are different claims. We need the same move in this parallel-flaw question: each individual case probably won't have a feature, so no case will have it. Keep both the individual-to-all move and the uncertain prediction in view.
Working the answers
- ACorrect
A single randomly drawn card probably won't be an ace. In an ordinary 52-card deck, only four cards are aces. But the aces are still there; drawing one is possible, and drawing through the whole deck would reveal them.
The individual card plays the role of the individual lottery ticket. Drawing an ace plays the role of getting a winning ticket. In both arguments, the unfavorable odds for a particular selection are treated as a reason to expect no successful selection at all. The mistake is expanding “probably not this one” into “none of them.”
- B
This also mishandles probability, but it stays with one race and one favored horse. A 999-in-1,000 chance of winning doesn't make another horse's victory impossible. B turns an extremely likely result into the only possible result.
The lottery argument instead starts with the outlook for each individual ticket and combines those separate outlooks into a claim about the whole collection. B lacks that individual-to-all move. A preserves it.
- C
This treats an extraordinarily unlikely sequence as something that never happens. That is not justified merely by the sequence's low probability. But the premise already concerns one complete sequence of 1,000 flips. It doesn't first assess each individual flip and then extend that assessment to every flip.
To match the lottery, we'd want separate predictions about individual cases being combined into a blanket prediction about all the cases. Don't let “1,000” and “never” substitute for that structure.
- D
This uses the result of earlier flips to predict the next one. The original never says the previous 1,000 tickets lost and therefore the next ticket must win. It moves from what is likely for any individual ticket to what is likely for the collection. Past outcomes making a future result seem due is a different idea.
- E
An average doesn't give every individual exactly that measurement. A group containing children above and below one meter could average one meter even if Pat's height differed from it. This assigns a group's average to one person. The original moves in the other direction, from individual expectations to a claim about the entire collection, and it doesn't involve an average height or any comparable measurement.
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