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What are the odds that a grandmother and her grand daughter are both leap year babies (born on Feb 29)?

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Assuming that leap year occurs once every four years, then the probability is Y^2=(1/(365*4+1))^2.

But in reality, there is a leap year every 4 years, unless the year is a multiple of 100 inwhich case it is a common year... unless the year is a multiple of 400 in which case it is a leap year.

So the probability of being born on February 29th is X = 1/(366*100+365*300-3). So the probability of both a grandmother and grand-daughter both being born on leap year is X^2.

But I would say that the probability of a grandmother having a grand-daugther 400 years younger is 0 (bold assumption) and the probability of having a grand-daughter 100 years young is negligibly close to zero, so their probabilities of being born on leap year are not the same.

Based on these assumptions, the probability I come up with is XY

Edited May 11, 2010 by Cantor

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2,134,521 to 1 for any two people. The grandmother/grand daughter angle is a red herring.

Edited May 11, 2010 by Joey D

[Guest]

  On 5/11/2010 at 5:46 PM, Cantor said:

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Assuming that leap year occurs once every four years, then the probability is Y^2=(1/(365*4+1))^2.

But in reality, there is a leap year every 4 years, unless the year is a multiple of 100 inwhich case it is a common year... unless the year is a multiple of 400 in which case it is a leap year.

So the probability of being born on February 29th is X = 1/(366*100+365*300-3). So the probability of both a grandmother and grand-daughter both being born on leap year is X^2.

But I would say that the probability of a grandmother having a grand-daugther 400 years younger is 0 (bold assumption) and the probability of having a grand-daughter 100 years younger is negligibly close to zero, so their probabilities of being born on leap year are not the same.

Based on these assumptions, the probability I come up with is XY

[Guest]

I see you did ask for odds and not probability so change my answer to (1/XY) : 1

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Too easy. Y^2=(1/(365*4+1))^2

  On 5/11/2010 at 5:20 PM, Lacel said:

What are the odds that a grandmother and her grand daughter are both leap year babies (born on Feb 29)?

[Guest]

Correction to my previous post. X = 397/(366*100+365*300-3). Since there are 397 leap years in a 400 year period.

[Glycereine]

  On 5/11/2010 at 6:44 PM, Cantor said:

Correction to my previous post. X = 397/(366*100+365*300-3). Since there are 397 leap years in a 400 year period.

I think you mean there are 97 leap years in a 400 year period?

[Guest]

  On 5/11/2010 at 7:12 PM, Glycereine said:

I think you mean there are 97 leap years in a 400 year period?

You are correct. That whole counting business always messes me up.

[Glycereine]

  On 5/11/2010 at 9:23 PM, Cantor said:

You are correct. That whole counting business always messes me up.

:-p