Comments on: Friday Puzzle

By: Answer to three-week-old Friday Puzzle (at wongaBlog)

Answer to three-week-old Friday Puzzle (at wongaBlog) — Fri, 20 Oct 2006 14:31:36 +0000

[...] A few weeks back I posted a Friday puzzle, and forgot to answer it. This was the question: You meet a woman and ask how many children she has; she replies “two.” You ask if she has any boys, and she replies “yes”. What is the probability of the other child also being a boy? [...]

By: Skuds

Skuds — Sat, 30 Sep 2006 01:40:18 +0000

Although I can follow Ben’s reasoning, I still think it is 50%

By: Simon

Simon — Fri, 29 Sep 2006 20:16:25 +0000

That second one is 50%.

The first question is similar to this. I put before you two boxes, each containing a child. I tell you one is a boy. In working out the probability the trap people will fall into is this: They will assign one of the boxes the boy and then consider the second box. They will fail to consider that the first box may have contained a girl and thus failed to acknowledge one of the three cases (if the first box contains a girl the second had to contain the boy).

The second question is more like me placing a single box containing a child in front of you and placing a boy next to it. Here there are only two cases and the boy is totally irrelevent.

By: Andrew

Andrew — Fri, 29 Sep 2006 19:39:04 +0000

That was my theory, yep. But let me ask you this:

You meet a woman and her son, and ask how many children she has; she replies “two.” What is the probability of the other child also being a boy?

By: Ben

Ben — Fri, 29 Sep 2006 19:15:05 +0000

In the population, there are three possible solutions: 2 girls, 1 boy and 1 girl or 2 boys. These are awarded probabilities 1/4, 1/2 and 1/4 respectively.
We know to discount the 2 girls option which leaves 1b1g and 2b. Probability of 2b is half that of 1b1g => 1/3 chance of the other child being a boy.

Any good?

By: Simon

Simon — Fri, 29 Sep 2006 19:14:01 +0000

But what were the colour of the interviewer’s socks?

By: Andrew

Andrew — Fri, 29 Sep 2006 17:23:13 +0000

Yes, but that’s not quite what the question is asking…

By: Clearly

Clearly — Fri, 29 Sep 2006 13:33:48 +0000

The chance of having either a boy or a girl is not dependent on the gender of any of their siblings.

If the chance of either gender is 50% then there is a 1 in 2 chance that the second child is a boy.