Paradoxes are worth fishing for; they are great in promoting
critical thinking (as you may notice I am avoiding the forbidden
word UNDERSTANDING).
Here is a paradox I found in a textbook to be used in Math-109.
It is based on the following data about airline departures, on-time
and delayed. Two airlines, A and B, were compared on the basis
of five airports, as below. Numbers in columns 2 and 3 refer to
on-time and delayed departures in a particular month. Column
4 shows %s of delays. The first table is for the airline
A while the next one is for B. I hope they will be
deformed too much by the Internet.
Note that the airline A beats airline B in every airport. On the
other hand the total for the airline A is 13.3 % (501 delays
out of 3775 departures) while the total for the airline B is
10.9% (787 delays out of 6438 departures). The author asks:
"How can it happen that A wins at every city but B wins
when we combine all the cities?"
Can you resolve this "paradox"?
A HINT IS BELOW THE SECOND TABLE.
DO NOT READ IT UNLESS YOU HAVE TO.
Table for airline A col 2 col 3 col 4
on-time delayed % del
Los Angeles 497 62 11.9
Phoenix 221 12 5.2
San Diego 212 20 8.6
San Francisco 503 102 16.9
Seattle 1841 305 14.2
Table for airline B col 2 col 3 col 4
on-time delayed % del
Los Angeles 694 117 14.4
Phoenix 4840 415 7.9
San Diego 383 65 14.5
San Francisco 320 129 28.7
Seattle 201 61 23.3
HINT: Scroll down after rereading the question.
Note that the airline A beats airline B in every airport. On the
other hand the total for the airline A is 13.3 % (501 delays
out of 3775 departures) while the total for the airline B is
10.9% (787 delays out of 6438 departures). The author asks:
"How can it happen that A wins at every city but B wins
when we combine all the cities?"
HINT: ---> The answer is in the data, and in what you
probably know about the weather patterns in different
places.