What Constitutes the Sample Space in a Birthday Probability Problem?

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Question:
Find out the birthday (month and day but not year) of a randomly chosen person. What is the sample space of the experiment. How many outcomes are in the event that the person is born in July?

Attempt:

We first must define the sample space. This is how I did it,

S = {JAN1, JAN2, ... , JAN31, FEB1, FEB2, ..., FEB28, ..., OTHER_MONTH_DAY_COMBINATIONS}

This can't be how I define it is it? This is not elegant in any way shape or form. Would someone push me in a better direction.

Now for the next question:
How many outcomes are in the event that the person is born in July?

There is 31 July outcomes.
 
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I believe it is that ugly, but you forgot something; people can be born on February 29th (leap years)
 
mattmns said:
I believe it is that ugly, but you forgot something; people can be born on February 29th (leap years)

:) - stupid leap years will get you every time.

Thanks mattmns, I appreciate the help!
 
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