# Utah woman gives birth to third consecutive Leap Day baby - Odds?

http://www.washingtonpost.com/national/utah-woman-gives-birth-on-third-consecutive-leap-day-ties-record-set-in-1960s-in-norway/2012/03/01/gIQAgGBtkR_story.html

This is beyond my math ability. Maybe another could give it a go?

What do you mean “odds”? It’s not like babies just pop out at random.

What are the odds any given female could produce three consecutive Leap Day births?

Well, considering they did it mostly on purpose, probably pretty good.

If we assume the birthday of your babies are randomly distributed, and leap days occur once every 1461 days, then the odds of three consecutive leap day babies is 1 in 1461^3, or 1 in 3,118,535,181. So, one in three billion. There are about three billion women on the planet, although not all of them have three children, so the odds that at least one woman on Earth would have three leap babies isn’t quite so unlikely.

You’d need to make some assumptions to get an answer, and a lot of the obvious assumptions probably aren’t very good ones. Are all days of birth in a year equally likely? Probably not. Maybe their wedding anniversary is around the end of May, or that’s the only time when her husband is home from an extensive travel job, or the like: That would mean that the end of February is a more likely time for all of her children to be born. Heck, maybe she’s actively trying to have Leap Day babies.

Assuming I’m reading my sources correctly, about 68% of births occur within a 4-week window centered around the expected due date. Let’s suppose that within that range, all the possible days are equal in probability (a conservative estimate). Therefore, hitting the day right on the dot has about a 2.4% probability, and doing it 3 times in a row has a 0.00143% probability. Small, but not unreasonably so: if a million couples tried it, about 14 would also get 3 in a row.

Of course this assumes they actually tried to hit those dates, and leaves out the uncertainties in conception. But I think it goes to show that it’s not as hard as it sounds.

Another thought:
Couples that have one leap baby (by chance) are probably more likely to try for more, essentially for the reasons in the article. If we stick to that subset of the population, the odds become better yet; something like 1 in 2000. There are around 5M leap babies out there already; it’s not hard to imagine that of their parents, over 2000 of the couples might intentionally try for more.

Thanks. I was just curious about HOW to solve the problem. Others ask good questions though.

So it might be more meaningful to look at all the days within the window of possibility for conception and birth 275 days before each birth (and multiply by three). The fact that it’s Leap Day doesn’t really matter, statistically speaking–that’s just an arbitrary target date. It would be the same statistical likelihood of trying to and succeeding in having a baby on Halloween, for example, three times. It could be in a row, or four years apart, or two years apart, etc. (Assuming, of course, birth isn’t induced.)

One thing that would influence the odds is a deliberately-induced birth. If it was done around the naturally expected birth date, there would be minimal health risks.

Even if there were randomness involved, the odds aren’t 1/1461^3 because you have to rule out any combinations that have two births within 36 weeks of each other (give or take a few weeks to take into account premature and late births).

there was a news story about mother and daughter being leap babies and i recall they gave odds at 2000000 to 1.

Another way of looking at it, assuming they weren’t deliberately trying for Leap Day with the first one, but were with the other two:

The probability of the first Leap Day baby is 1 in 1461.

For number 2, the probability of her getting pregnant in the relevant month is somewhere around 1 in 4 (if I remember right, isn’t that the probability for a normally fertile couple in any given cycle?). Once she’s pregnant, going by Dr Strangelove’s figures, the probability of that baby actually arriving on Leap Day (assuming no induction/Caesarean) is around 1 in 30. So the probability of #2 arriving on the next Leap Day is around 1 in 120.

Same for #3: 1 in 120.

So the overall probability would be around 1 in 21 million. My figures are very rough - jjst tossing them out there for the sake of another way of looking at the probabilities.

Since the statistics have been covered…

Trying to conceive a baby for a particular birth date isn’t anything I have a problem with in general. But leap day or no leap day, trying to get a younger sibling to share a birthday with an older sibling is just tough on your kids. As is intentionally trying to have a Christmas baby.

Everybody deserves to have their own special day, IMHO.

Right–that would be assuming that once one baby is born, they immediately start trying for the next one. This isn’t going to happen if they want one particular date, because they won’t try to conceive until the window comes up for that date, which will be a while because that window comes up every 52 weeks.

Exactly. First they’re going for a day that only comes around once every four years, which creates its own issues. In their family, they might make a big special deal about the leap day birthdays, but that doesn’t mean that friends and classmates will do the same. You’re setting the kids up to have to explain their birthday, choose another day, endure jokes about their age, etc. On top of that they’re going to have the same birthday as their obnoxious little sister or older brother. I personally hate those “let’s have a big party in March to cover the March and April birthdays” approaches.

Having 3 leap babies is a pretty good idea. Just think of all the money the parents save on birthday gifts. Plus with 3 kids all with Feb 29 birthday, they only need to buy 1 cake every 4 years.