Self-study
Support For any given ticket in a 1000-ticket lottery, it is reasonable to believe that that ticket will lose. ██████ ██ ██ ██████████ ██ ███████ ████ ██ ██████ ████ ████
Method of Reasoning
The author concludes that it’s likely no item in a set will have a property (being a winning ticket). His reasoning is that each individual item (lottery ticket) is unlikely to have that property.
Identify and Describe Flaw
This is the cookie-cutter flaw of confusing the properties of a part with properties of the whole. Just because each individual lottery ticket is unlikely to be a winner, it doesn’t mean that the lottery as a whole is unlikely to have a winner.
3.
Which one of the following ████████ ██████ █████████ ████ ███████ ██ ███ ██████ █████████ ██ ███ ████████ ██████
a
It is reasonable ██ ███████ ███ ███ ████████ █████ ███████ ████ ████ ██ ████ ███ ██ ██ ████ ██ ██ ██ ██████████ ██ ███████ ████ ██ ███ ████ █████ ██ ██████
(A) concludes it’s likely that no item in a set will have a property (being an ace). The reasoning is that each individual item (drawn card) is unlikely to have that property.
This is the same cookie-cutter flaw of confusing part and whole that we saw in the stimulus. Just because no individual card is likely to be an ace, it doesn’t mean that it’s likely to never draw an ace.
b
When the chances ██ █ ███████ █████ ███████ ███ ████ ███ ███ ███ ██ █████ ██ ██ ██████████ ██ ███████ ████ ████ █████ ████ ████ ██ ██ ██ ██████████ ██ ███████ ████ ██ ███ █████ ████ ████ █████ ███ ████
This is the wrong flaw. (B) is conflating high probability (999/1000 chance) with absolute certainty (1000/1000 chance). (I.e., even if it’s very unlikely, it’s still possible that another horse could win.) By contrast, the stimulus commits the cookie-cutter flaw of confusing properties of a part with properties of the whole.
c
It is unreasonable ██ ███████ ████ ████ ███████████ ████ █████ ████ ████ ██ ██████ ██ ██ ██ ██████████ ██ ███████ ████ ████ █████ ████████
This is the wrong flaw. (C) erroneously concludes that, because 1000 consecutive results of heads is unlikely, it’s impossible. But the phenomenon being considered—a result of 1000 consecutive heads—remains the same. By contrast, the stimulus mistakenly switches between considering a property of individual lottery tickets and a property of the lottery as a whole.
d
It is reasonable ██ ███████ ████ ██ ███ ████ ██████ ████ ██ █ █████ ████ ███ ██████ ███ ████ ████ ████ ██ ██████ ██ ██ █ ████ ███ ██████ ██ █████ ███ ████ ████ █████ ██ ███ ████████ ██ ██ ██████████ ██ ███████ ████ ██ ████ ████ ██ █████ ███ ████ ████ ██ ██ ████████
This is the wrong flaw. If the principle that heads follow tails didn’t apply to the previous 1000 flips of this coin, there’s no reason to suppose it will apply to the 1001st. By contrast, the stimulus commits the cookie-cutter flaw of confusing properties of a part with properties of the whole.
e
For any given █████ ██ █████████████ █████████ ███ ███████ ██████ ██ ███ ██████ ██ ██ ██ ██████████ ██ ███████ ████ ██ ███ ██ ████ █████ ████ ███ ██ ███████ ███ █████ █████
This is the wrong flaw. (E) mistakenly assumes that a property of the group (average height) can be automatically applied to every member of the group. By contrast, the stimulus erroneously applies a property of individual members of the group (unlikely to win) to the group as a whole.