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*From*: Carl Mungan <mungan@usna.edu>*Date*: Tue, 28 Oct 2014 09:05:30 -0400

We've discussed problems similar to the following one before. (Look up

"two aces" in the archives.) If you think there are ambiguities in how

I have worded things below, feel free to reword them. The issue I am

interested in is not the semantics, but how additional information

affects probabilities p.

Consider all two-child families in the world such that X. What

fraction of those families have two boys?

Substitute X with one of the following statements:

case A) "at least one child is a boy"

case B) "at least one child is a boy born on a Tuesday"

case C) "the older child is a boy"

case D) "the older child is a boy born on a Tuesday"

(Assume equal probability that any baby is a boy as a girl, and equal

probability that a baby is born on any day of the week.)

Hypothesis: Providing additional positive information that is relevant

will increase the fraction. (By "positive" I mean you're not giving me

information about girls in families rather than boys. By "relevant" I

mean you're not for example telling me "It rained on March 21, 2008 in

Knoxville.")

What I find is that that p(B) > p(A) and p(C) > p(A) which both

support the hypothesis. However, I also find p(C) = p(D) which

contradicts it. So apparently (and surprisingly to me) the hypothesis

is false.

Feel free to think about what the fractions (probabilities) are before

you peek at this solution:

http://usna.edu/Users/physics/mungan/_files/documents/Scholarship/ProblemOfTwoBoys.pdf

Please feel free to comment and challenge anything I've said here. I'd

like to clarify better ways to think about these kinds of probability

problems. -Carl

--

Carl E Mungan, Assoc Prof of Physics 410-293-6680 (O) -3729 (F)

Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363

mailto:mungan@usna.edu http://usna.edu/Users/physics/mungan/

**Follow-Ups**:**Re: [Phys-L] two boy problems***From:*John Denker <jsd@av8n.com>

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