Thinking traps

Imagine that there is a lethal disease which has no cure. The disease is contagious but only affects 1 in 10,000. You’re worried so you decide to go to the doctors to be tested. The doctor informs you that the test is 99% accurate (In other words it will deliver a correct positive or negative result 99% of the time) and should take about two weeks to get the results, which will be posted to you. Two weeks pass and a letter drops onto the mat. It’s from the clinic. You open the letter to discover that you have been diagnosed with the disease.

Review the above scenario and ask yourself the following question:

What are the chances that you have the disease? Please come to a decision before reading on

If you of the opinion that you are very likely to have the disease you would be wrong. That’s right, WRONG!
If you think that it’s very unlikely that you have the disease congratulations, you’re right. Give yourself a pat on the back and you may be excused and I’ll see you next week.

Now, for everyone that’s still here let me explain. There was probably one small, but vital, piece of information that maybe you hadn’t factored in. The deadly disease only affects 1 in 10,000 people. So right from the start you see you only have a 1:10,000 chance of catching it. So let’s say that 10,000 people go for blood tests only 1 person will be correctly diagnosed as having the disease. But about 100 people will be diagnosed as having it when in actual fact they don’t. Because the test is only 99% accurate that means that 1% of the 10,000 (100) will receive a false positive. So you are about 100 times more likely to be in misdiagnosed category.

The problem above isn’t just a clever game. It has the potential to be a life changing event that could have disastrous consequences.

Let’s try another:

I pull out 5 cards, at random, from a shuffled deck 3 times and I note the results:

1) 2 of clubs, 5 of spades, Jack of hearts, 7 of Diamonds and 4 of clubs

2) 10 of Hearts, Jack of Hearts, Queen of hearts, King of hearts and Ace of hearts

3) 6 of Spades, 7 of spades, 8 of spades, 9 of spades and 10 of spades

Which of the three sets is more likely? Be honest.
My gut tells me that the first sequence would be more likely. Any poker player will recognise the Royal flush and the Straight flush which came out second and third. But the truth is they are all as probable as each other. It’s only the randomised sequence of number one which leads us to believe that that is more probable. If there are any mathematicians reading this I would love to know what the odds of pulling anyone of these sequences out are. 500,000: 1 is my guess.

Much like lottery results. You are just as likely to have the winning numbers be: 1 2 3 4 5 6 as you are any other combination. About 14 million to 1. And just so we’re clear, no, somebody does not have to win. Just like a coin will always have a 50/50 chance of landing on heads or tails. Unless it’s in the hands of a hustler who can control the coin.

Cognitive illusions can be fun games. But they can also highlight the kinds of thinking traps that we all fall into; which in turn can lead to dangerous thinking and give life to ideas that can have deadly consequences. Please turn your head towards New York which is currently going through a measles outbreak not helped, I’m sure, by the anti-vaccination movement.

Just as you cannot do very much carpentry with your bare hands, there is not much thinking you can do with your bare brain.

Anyone wanting to look more into thinking can’t go far wrong with Daniel C Dennett’s book “Intuition pumps. Tools for thinking”


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