Interesting math problem

I was just perusing a few old articles and came across a math problem that interested me the first time I saw it.
In order to show I mean well as the *s rack up, I will post something substantive, and well placed.
Here goes

A market researcher needs to interview married couples for a certain survey. The researcher arrives at a house with three apartments. From the names on the mailboxes downstairs, the interviewer knows that only one of the three apartments has a married couple living in it. The others have two men, and two women living in them, respectively. But when the reseaercher goes upstairs to the apartments, the doors are unmarked and it is impossile to tell which of the apartments is which. Therefore, the prior probability of knocking on the right door (that of the married couple) is clearly 1/3. The researcher knocks on a door, and a woman answers. What is now the probability that the researcher has reached the married couple?

Four unreasonable assumptions

1) If the researcher reached the apartment of the married couple, then there is a 50/50 chance that either person answers the door, meaning that given the married couple ws reached, the chance that a woman answers the door is %50.

2) If the researcher reached the apartment with the two men, then there is a zero probability that a woman will answer the door(assmming no visitors).

3) If the researcher reaches the apartment of the two women, then there is a one hundred percent probability that a woman will answer the door(again no visitors).

4)The prior probabilities-meaning the probabilities prior to the event that a woman answered-of reaching the married couple, the two men, or the two women, are all one third each.

[ThinkQuick]

See 2 boxes problem, 2 posts ago

Because of the symmetry it does not matter if a male or female answers. No additional information is given and therefore the initial probability does not change. [img]/images/graemlins/smile.gif[/img]

You guys have no problem with these I see. at uni this stumped my calc 3 class.

Cambraceres< needs to come up with better math problems

[ohnonotthat]

Well, since you were stumped by the NSFW rule I wouldn't look down my nose at the calculus crew. [img]/images/graemlins/shocked.gif[/img]

BTW, wanna pull my finger ? [img]/images/graemlins/mad.gif[/img] [img]/images/graemlins/grin.gif[/img]