PrepTest 112, Section 3, Question 21
Sandy: I play the Bigbucks lottery—that's the one(78 more words not shown)
Which one of the following(14 more words not shown)
- ASandy holds that(15 more words not shown)
- BAlex holds that(14 more words not shown)
- CSandy holds that(13 more words not shown)
- DAlex holds that(19 more words not shown)
- ESandy holds that(20 more words not shown)
Reading the argument
A bigger pot sounds appealing. But how many people might share it with you?
Sandy is right that the pot grows after weeks without a winner. I still want to know whether that larger prize attracts more players, including more people who might choose the same winning numbers. A bigger total prize doesn't necessarily mean a bigger share for each winner. Imagine a million-dollar pot with one winner versus a three-million-dollar pot shared by six winners. The larger pot gives each winner less.
Alex notices the number of players, but uses it to make a different claim: Sandy is more likely to win when fewer other people play. Why would someone else's ticket change whether Sandy's five numbers are drawn? This isn't a drawing that selects one winning ticket from all the tickets purchased. Everyone who picks the five drawn numbers shares the pot.
What we’re looking for
The question asks for a mistake by either speaker. My clearest prediction is Alex's confusion between the chance of matching the numbers and the amount a winner receives. Fewer other players might reduce sharing without making Sandy's chosen numbers more likely to appear.
Working the answers
- A
Sandy recommends choosing when to play based on the pot's size. Sandy doesn't say playing repeatedly has no effect on the chance of winning at least once. A claim about the number of times a person enters isn't part of the reasoning given.
- BCorrect
Alex treats fewer competing players as a reason Sandy is more likely to win. But the winning numbers are drawn independently of how many people picked them. Sandy wins by matching those numbers, whether nobody else matches or many people do.
Other winners matter to the split of the prize. They don't stop Sandy's matching selection from being a winning selection. That is why the number of other players doesn't establish Alex's claim about Sandy's chance.
- C
The pot's size doesn't itself change the chance that a particular set of five numbers will be drawn. Sandy's stated reason for preferring the larger pot concerns the available money. C doesn't identify a mistake in that distinction.
- D
Alex actually links smaller pots, fewer players and a greater chance of winning. Since a week without a winner increases the pot, Alex's reasoning doesn't treat that history as irrelevant in the way D says. More fundamentally, independence from a prior winner wouldn't itself be the mistake here; Alex's appeal to the number of players is.
- E
Sandy says the money pot increases, not that the chance of a winner increases. Waiting for a larger prize doesn't by itself commit Sandy to thinking a win is now due. E substitutes a claim about probability for Sandy's claim about the prize.
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