Friday Puzzle

September 29th, 2006 - 14:16 | 8 comments

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?

There are no tricks here, it’s pure logic (assume a 50% chance for each gender). From The Skeptics’ Guide. The answer raises an interesting further question, which I’ll post in due course.

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8 Responses to “Friday Puzzle”

1 Clearly Sep 29th, 2006 at 2:33 pm

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.
2 Andrew Sep 29th, 2006 at 6:23 pm

Yes, but that’s not quite what the question is asking…
3 Simon Sep 29th, 2006 at 8:14 pm

But what were the colour of the interviewer’s socks?
4 Ben Sep 29th, 2006 at 8:15 pm

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?
5 Andrew Sep 29th, 2006 at 8:39 pm

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?
6 Simon Sep 29th, 2006 at 9:16 pm

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.
7 Skuds Sep 30th, 2006 at 2:40 am

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

1 Answer to three-week-old Friday Puzzle (at wongaBlog) Pingback on Oct 20th, 2006 at 3:31 pm

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