Examples and fallacies
A fallacy is a mistake in reasoning. The following examples
each contain some reasoning about probabilities, some of which
is correct and some of which is mistaken. See if you can spot
any mistake, and then click "correct" if you think the
reasoning is o.k. and "fallacy" if you think it is wrong.
- Fred is playing roulette in a Macau casino. The
roulette wheel has 36 numbers (ignoring the zero), of which
half are red and half are black. Fred reasons as follows: In
the last ten spins, all the winning numbers have been red.
But on average, only half the winning numbers are red. So to
even things out, there must be more black numbers than red
numbers coming up. So I stand a better chance of winning if I
bet on black.
Correct or fallacy?
- The chance of the Mark Six numbers being exactly the
same two days in a row is extremely small. So to maximize my
chances of winning today, I should not choose yesterday's
winning numbers.
Correct or fallacy?
- Suppose I am at the Pokfield Road bus terminus, waiting
for the number 23 bus to leave for North Point. The number 23
leaves from here every 8 minutes. So the longer I wait for
the bus, the higher the probability that it will leave in the
next minute.
Correct or fallacy?
- A city has a crackdown on speeding drivers, and the
number of traffic fatalities falls by 12%. The local
government claims that the increased enforcement has saved
lives. But the crackdown was started because of a sudden
increase in traffic fatalities the prior year. After an
unusually high value, the number of deaths is likely to fall
the following year anyway. So there is no reason to think
that the crackdown caused the decrease in fatalities.
Correct or fallacy?
- "BALTIMORE (AP) A Maryland woman this week gave birth to
triplets for the second time in less than two years, defying
odds of about one in 50 million, hospital officials said."
The reasoning here is that since only about one birth in seven
thousand is of triplets, the odds of having two sets of
triplets in a row is about one in 70002, which is one in 50 million.
Correct or fallacy?