Thread by @ProfDFrancis

A question that I thought was simple, has had enormous pushback from respondents. 50:50 are ardently espousing an answer I consider to be obviously wrong.

Suppose there is a shop which only lets you in if you bring exactly ONE child.

Each person going shopping has two children, and chooses one child to go with them, but ALWAYS takes a boy if they have a boy.

For a randomly chosen customer in the shop, if their accompanying child is a boy, what is the probability that the child at home is a girl?

Let's give it a few days to see how people vote.

Please don't give the answer away, as it will spoil the experience.

Great question from Wes Pegden!

Actually no, didn't mean that. It doesn't matter if they choose randomly or not.

8-)

At 300 votes, amusingly:

about half voted for "1/2", and
about one third voted for "1/3".

Now let me make it much easier for you all.

Please note that the following is ONLY TO MAKE IT MUCH EASIER TO SEE THE CORRECT ANSWER.

It is not a political statement.

Officer Francis works in a neighbourhood where half the people are white and half are black.

The people themselves do not segregate racially, and mingle with perfect equanimity.

But whenever Officer Francis sees two people walking down the street, AT LEAST ONE OF WHOM IS BLACK,

Whenever Officer Francis sees two people walking down the street, AT LEAST ONE OF WHOM IS BLACK,

Officer Francis's policy is to automatically SHOOT DEAD A BLACK PERSON and let the other one go.

What proportion of the SURVIVORS of these shootings will be black?

As predicted, people are finding this MUCH easier!

100% correct among the first 6 voters.

The following possibilities are all EQUALLY likely:

First child Second child
Boy Boy
Boy Girl
Girl Boy
Girl Girl

From 400 parents, 100 with each of the four child sequences, how many fit my description of "brought a boy"?

Remember the parents always choose a boy if they have one.

First Second
Boy Boy --> Brought a boy
Boy Girl --> Brought a boy
Girl Boy --> Brought a boy
Girl Girl --> Brought a girl

Only the 300 parents in the top 3 categories have brought a boy.

Children Brought At home
B B B B
B G B G
G B B G

So, of the parents you see with a boy, what proportion have a girl at home?

OK Great!

With some easy steps of reasoning, I hope the correct answer is now obvious.

Erratum, in the first question in the thread, at 300 votes:

Half of people voted for "1/2", and
A THIRD voted for (the correct answer) "2/3".

I am disappointed that the shooting-black-people-preferentially question didn't get 100% correct answers, namely that the SURVIVOR is more likely to be white than black.

The principle is the same. Let's say 100 pairs of 2 people are walking down the street, side by side.

Left Right

White White
White Black
Black White
Black Black

100 of each of the above pair types.

The 100 pairs of white people receive merely a nod hello.

White White --> "How d'you do?"

However 300 of the pairs experience a shooting. Of course it is entirely justified as one of them was looking at me strangely, your honour.

White Black -> White person escapes
Black White -> White person escapes
Black White -> Black person escapes

I should emphasise that I am in reality not in favour of shooting anyone, of any skin type.

I limit my anger to sending slightly intemperate emails, and such like.

More fun puzzles here:

tweetorials.inspirion.org/h2/17c43f25b31…