Self-study
Travel writer: Conclusion A vacationer should choose an airline that has had an accident in the past 5 years. ██████ ████ ███ ████ █████████████████ ███████ ████ ████ ███ ███████ ███████ ███ █ ████████ █████ █ ██████ ██ ██ ██ ███████ ███ ███ ██ ████████ ██████ ███ ████ █ ██████ ███ ███████ ████ ███ ███████ ████ ████ █ █████ ███ ██████████
Method of Reasoning
The travel writer knows that the average airline has 1 accident every 5 years, and so concludes that each individual airline is likely to have roughly 1 crash every 5 years—if there’s been a crash in the past 5 years, the airline probably isn’t due for another one yet.
Identify and Describe Flaw
This is a misunderstanding of averages! It’s quite possible that one airline could have a lot more than 1 crash every 5 years, and a bunch of other airlines have 0 crashes every 5 years to balance out the average. Don’t take the travel writer’s advice—try to fly with airlines that don’t crash very often!
8.
The flawed reasoning in the ██████ ████████ ████████ ██ ████ ███████ ██ ████ ██ █████ ███ ██ ███ █████████ ██████████
a
A tossed coin ███ ████ ██ █████ ███ █████ ██ █ ████ ██ ██ █████████ ██████████ ██ ███████ ████ ███ ████ ██ ███ █████ ███ ████ ████ ██ ██ ████ ██████ ██ ████ ██ █████ ████ █████ ████ ██ ██ ███████ ██████
Wrong flaw. This isn’t a valid argument, because it’s theoretically possible that a fair coin could come up heads 100 times in a row. But unlike the stimulus, (A) doesn’t make a prediction about the future based on an erroneous understanding of averages.
b
If there are ██ █████ ████ ███████ ██ █ ██████ ███ ██████ ██ ██ ███████ █████ ████ ██████ █████████ ██ █████████ ██ ███ █████ ████ ██ █ ██ ███ █████ ██ ██ █████ ████ ██████ ███ ████ ██ ███ █████ ████ ████ ██ █████ ███ ███ █████ ████████ ██ ██████████ ████ ███ ██████ ██ ███ █████ ██ ██ ███ ██████ ████ █ ██ ███
Adult male baboons in a group of 10 have an average chance of 1 in 10 of ascending to dominance. Like the stimulus, the author uses an average to make a prediction about an individual: if a baboon hasn’t ascended in the past 10 years, he’s probably due for dominance. But that’s a misunderstanding of averages. Maybe one baboon has a 91% chance of ascending to dominance and the 9 other baboons each have a 1% chance—the average chance is still 1 in 10, but you’d want to put your money on the 91% baboon!
c
On a given ████ ██ ███████ ██████████ ██████ ██ █████ ████████ ██ █ ███████ ████████ ██ █ ███████ ████ ██ █ ██ ███████ ██████████ ███ ██████ ██ ██████ █ ██████████ █████████ █████ ████████ ██ █ ███████ ████████ ██ ███ ████ ██ ███ █████ ███ ██ ████ █ ██ ███████
Wrong flaw. This isn’t a valid argument, because we don’t know much about Marty—maybe he’s a reckless tricycle rider with a higher than average chance of being in a traffic accident, or maybe he never leaves the house and has a 0% chance! Regardless, (C) doesn’t commit the same flaw as the stimulus, which assumes that it’s possible to combine historical data about an individual with average statistics about a group to make predictions about the individual’s future.
d
The average adolescent ███ █████ █████████ ██ █ ███████ ███████ █████ █████ ██ █████ ███ █████ ██████ ████ ██ █████ ███ █████ █████████ █████ ██████ ██████████ █████ ██ ████ ███████ ███ ███████ ██████████ ███ █████ █████████ █████ ████ ████ ███ ███████ ██████████ ███ █████ ██████████ ███ ███████ ██████████ ███ █████ █████████ █████ ████ ████ ██ █████ ███ █████ ██████ ████ ██ ██ ████████ ██████
No flaw. This is a valid argument! If the average adolescent who works full-time makes around 76 cents for every dollar a fully employed adult makes, and the average adolescent who works part-time makes less than the average adolescent who works full-time, then the average adolescent who works part-time must make less than the average employed adult (assuming that the adult’s employment is full-time).
e
Though until recently ████ █████ ███████████ ███ █████████ ██ ███████ ████ █ ████ ████ █ ████ ██ ███ █████ ██ ███ ███████ ██████████ ██ ███ █████████ ██ ████ █ ████ ████ █ ██ ███████ ██ ███ █████ █████ ██ ███ ████ ████ ██ ███ ███████ ███████████ ██ ██ ██ ███████ ██████ ██ ███████ ██ ████ █ ████ ████ ██
Wrong flaw. While we can’t validly conclude that the grandmaster will maintain the same likelihood he has been exhibiting of responding to move X with move Y, (D) doesn’t commit the same flaw as the stimulus, which assumes that it’s possible to combine historical data about an individual with average statistics about a group to make predictions about the individual’s future.