Probability puzzler!

I'm not sure which forum this belongs in, so...

Two people saunter into a Vegas wedding chapel and announce that they want to get married. When asked, they each say they were born on Feb. 29. They don't mention their birth years.

What are the odds of that, that they were each born on a Leap Day (not necessarily the same year)?

If I can assume they are both being honest about being born on February 29th. Then the probability of them both being born on a leap year is basically 100%. Because February 29th only takes place on leap years.  

(This is admittedly a smart-ass answer and probably not what you were going for but I couldn't resist). 

1 in 2,134,521

As the question is posed, I believe LiveFreeNW is correct.

Candy

Uh, no. First of all, if you were born on a Leap Day, Feb. 29, as I said, you were obviously born during a Leap Year. What I asked was what was the possibility that a couple who walked into a wedding chapel were each born on a Leap Day. Not necessarily the SAME Leap Day.

I could have just said "Any two randomly chosen people."

I'll post the answer below.

This is a parlay. First of all, what is the likelihood that at least one of them was born on a Leap Day? Then, what is the likelihood that the other person was also born on a Leap Day?

Like any parlay (two or more things have to happen), you multiply the probabilities together. For instance, what are the odds against rolling a twelve? Two things have to happen, and the probability of each is 1/6. So multiply 1/6 x 1/6; 1/36.

There is one Leap Day every four years; those four years consist of (3x365) + 366 days. 1,461 days. So the chances of Person One having been born are 1 in 1,461. Ditto for Person Two.

The odds of this parlay are 1/1,461 x 1/1,461. 1,461 squared is 2,134,531. So, jstewart is correct.

 I could be wrong here so asking for clarification. I think your formula of (3x365)+366 is presuming that there is only four years worth of days in which the individual could have been born. This only works if the individual in question is four years old. For an accurate formula wouldn't you have to know the age of the individual in question? Wouldn't you need to know how many days they've been alive? Something like (365x36)+(366x3)+number of days since last birthday. 

I am admittedly not a math guy so I don't necessarily think I am right but hoping someone can explain how I am wrong. 

If one in four x's is something (in this case, a leap year), then the chance of an x being something is 25% no matter what the sample size may be. Any four years will contain exactly one leap year.

Likewise, any consecutive 1,461 days will contain exactly one Leap Day.

The length of the individual's life is irrelevant, just as the chance of a coin flip coming up heads is 1/2 whether you flip it once or 1,000 times.

Also, if an individual is born, his chance of having been born on that day doesn't increase as he gets older, right? The probability has already been determined.

 But the reason the coin flip is 1/2 is that there are only two possibilities. Heads or tails.(Assuming we eliminate the near zero chance of it landing on an edge) However if I asked someone thier birthday there are more than 2,134,521 possible answers.