Reasoning Traps

Do you think that when you try to reason the correct answer that you are really thinking logically? Do you always make the best decisions? Here are some Common traps people fall into when reasoning.

The Gambler's Fallacy

If you have a coin and flip it 7 times, and it came out tails every time is there more of a chance it will come out a certain way on the next flip?

Some people would say it would be more likely to come out heads. Since the ratio of heads to tails it 1:1, the 7 tails would need to be balanced out by 7 heads so it is
more probable that heads will come out.

Wrong!

Every flip is independent of any other. Therefore, every time you flip the coin there is an equal chance of it landing on heads or tails. It is true that eventually the flips will end up 50/50, but probability cannot be applied to any single event. Probability is only intended on predicting a string of flips and not each individual flip.

The Law of Small Numbers

A subject reaches into a pot and grabs out 4 green beans and 1 red bean. Then the beans are put back and a second person grabs 23 green beans and 15 red beads. Both conclude that there are more green beans in the pot, but which one has better evidence?

Most people would conclude that the first person has better evidence because the ratio of green to red beans that he pulled was 4 : 1. This would suggest there are more green beans, but the odds of having more green in the second example are much higher. Since the second person's sample is so much larger, there is much less of the chance factor involved.

Small numbers have a much greater chance of giving misleading and not accurate results.

Most people see that large samples are better, but few really understand how much results in small numbers can vary and be unrepresentative. This belief in small numbers also explains why people generalize things after only experiencing a few cases.

Predicting the Improbable

Which causes more deaths?

Accident falls or gun accidents?
Tuberculosis or floods?
Suicide or murder?
Asthma or tornadoes?

Actually, the first answer in each of these pairs causes more deaths. Don't feel bad if you got some of these wrong. People frequently tend to overestimate the improbable. If has been shown that people seem to predict these events higher because they are dramatic and get high media coverage, although they are very infrequent. Fatalities from disease on the other hand, tend to be underestimated. Interestingly, many researchers believe that people overestimate these high media things because they are fresh in people's memory from reading about them or seeing them on the news.