# davesainsbury.com

personal website

## What creates that feeling that we know something?

A simple thought experiment.

It is “Fathers of Daughters” day in the park.
Only men with daughters are allowed.
One of these men asks you,  “I have at two children, one is a girl, what is the probability that my other child is a girl?”
Assuming equal birth frequencies, it would seem obvious that the chance is 50:50 that his other child is a girl.

Why does this answer feel correct?
When, in fact, it is wrong!
You can scroll down the page for the explanation and some variations on this “cognitive illusion”.

It is similar an optical illusion.

Both A and B squares are identical shades of grey.

Somehow we feel OK about an optical illusion, perhaps because we can cover up the other squares and prove it is an illusion.
But we may remain argumentative about a cognitive illusion, perhaps because it challenges the very mechanism we are using to make judgements.

Why does this matter?
We (and our patients) are at our must vulnerable when we are convinced we know, when we are attached to a belief.
This is called “task fixation” in airline crash investigation.

This is another characteristic of “being in the world” (In-derWeltsein) that is “made sense of” by “dual process theory”.

This is an eloquent exposition

Or perhaps, if you still think you are in control of your own thoughts

## More on the father daughter problem

The man in the park is drawn from a very special population.
Families with at least one girl.
Assuming an equal frequency of births then the following patterns are equally possible.
Girl Girl, Boy Girl, Girl Boy.
So the probability of having met a man with 2 girls is 1 in 3

Let us say that you are walking home from the park and you meet another man, walking with a girl.
He tells you, “I have two children, one of whom is a girl” and asks, “What is the probability that my other child is a girl?”
There is debate on the answer to this question, although the majority favour 1 in 3

He tells you, “I have two children, this girl is my daughter”, and asks “What is the probability that my other child is a girl”
Now our instinct is correct, the probability is 1 in 2.
He is drawn from a population of men walking a daughter,
assuming walking with a child of either sex is equally likely.
Assuming that the first-born child has an equal probability of being a girl or a boy &
the second-born child has an equal probability of being a boy or a girl
The population from which the father and daughter combination is drawn is now
First-born child girl walking, second-born child girl at home
Second-born child girl walking, first-born child girl at home
First-born child girl walking, second-born child boy at home
Second-born child girl walking, first-born child boy at home

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