Self-study
Sandy: I play the Bigbucks lottery—that's the one where you pick five numbers and all the players who have picked the five numbers drawn at the end of the week share the money pot. ███ ████ ████ ██ ████ ████ █████ █████ ████ ████ █ ███ █████ ████ ██ ████████ ███████ ███ █████ ███ █████████ ████ ████ ████ █████ ██ ██ ███████
█████ ███ ██████ ████ ██████ ██ ███ ███ ███████ ████ ███ █████ ███ ██ ██████ ███████ ██████ ████ ███ ██████ █████ ██████ ███ ████████
Summarize Argument: Counter-Position
Alex implicitly concludes that Sandy should not play the Bigbucks lottery when the pot is larger. He supports this by saying Sandy is more likely to win when the pot is small, since that’s when the fewest people are playing.
Identify and Describe Flaw
Alex’s reasoning is mistaken because he doesn’t understand how the Bigbucks lottery works. To play, Sandy picks five numbers, and if they match the winning numbers, she shares the prize with anyone else who also picks correctly.
Alex thinks Sandy is more likely to win when fewer people play, but that’s not true. Her chance of picking the correct five numbers doesn't depend on how many other people are playing. The number of other players may affect how many people she’d have to split the pot with, but it doesn’t affect her individual chance of winning.
21.
Which one of the following ████ ██████████ █████████ █ ███████ ██ ███ █████████ ██ ███ ██ ███ ███ █████████
a
Sandy holds that ███ ███████ ██ ████████ ███████ ███ ██████████ ██ ███ ██████ ██ █████ ████ ██████ ██████
Like (C), Sandy never makes any claims about the chances of winning, nor does she claim that her chance of winning is unaffected by the number of times she plays. She just argues that it’s best to play when there’s a bigger pot.
b
Alex holds that ███ ███████ ██ ███████ ███████ ███ ████████ ██ ███ ██████ ██ █████ ██████ ████████
This describes a mistake in Alex’s reasoning. He thinks that Sandy is more likely to win when fewer people play. But actually, her chances of picking the correct five numbers are the same— extremely low— regardless of how many other players there are.
c
Sandy holds that ███ ███████ ██ ████████ ███████ ███ ██████████ ██ ███ ████ ██ ███ ████
Like (A), Sandy never makes any claims about the chances of winning. Also, it’s true that the chances of anyone’s winning are unaffected by the size of the pot. So even if she did hold this, it wouldn’t be a mistake in her reasoning.
d
Alex holds that ███ ███████ ██ ███████ ███████ ██ █ █████ ████ ███ ██████████ ██ ███████ ██████ ███ ███ ███ ████ ███████
Alex never makes this claim. But even if he did, it wouldn’t describe a mistake in his reasoning because it’s true that Sandy’s chances of winning in a given week are unaffected by whether someone won the week before.
e
Sandy holds that ███ ███████ ██ █████ █████ █ ██████ ██ ██ ██ ██ ███ ███ ███ ███ ███████ ███ █████ █ ██████
Sandy never claims that the chance of there being a winner goes up if no one has won in a while. She just argues that it’s best to play after no one has won in a while, because that’s when the pot is biggest.