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        riddles >> easy >> Leap Year Birthdays
        
(Message started by: SWF on Nov 14^th, 2003, 9:35pm)

Title: Leap Year Birthdays
Post by SWF on Nov 14^th, 2003, 9:35pm

Sally's birthday is February 29. She has one brother and one sister. Estimate the probability that at least one of her siblings also has a birthday on February 29.

Title: Re: Leap Year Birthdays
Post by NickH on Nov 15^th, 2003, 9:15am

An interesting open-ended question!

Here is a list of relevant factors that springs to mind...

::[hide]The rate of twin and higher multiple births in the relevant population. This is clearly more significant when the date in question is February 29th than it would be otherwise.

Also important may be the probability that someone with the name 'Sally' is from a particular country and/or ethnic/racial/cultural group, if the rate of multiple births is higher in some groups than in others. For example, Sally is probably not Chinese, which is relevant if twins are markedly more or less common in China.

If Sally is not a twin, then we must consider the probability that a sibling would be 4, 8, 12, ... years older or younger. An age gap of 8 years or more is unusual in some cultures.

Sally's age may also be significant, if a wide age gap was once more common. The name 'Sally' may itself give us some information about her age. (Perhaps it was once much more common than it is now.)

I'm sure there are other relevant factors. However, the rate of multiple births in the US is currently about 3%, up more than 50% since 1980. (See below.) Considering the 1000+ day age difference for non-twins, I think the twin factor accounts for most of the probability that Sally has a sibling with birthday February 29th. Because the twin rate has significantly increased recently, we should weight the probability by the changing popularity of the name 'Sally' over the last century or so.

My best guess: between 1/50 and 1/40.

Nick[/hide]::

http://www.nomotc.org/library/incidence.html

Title: Re: Leap Year Birthdays
Post by visitor on Nov 15^th, 2003, 10:26am

You forgot one very big factor: [hide]
The possibility one of the younger children was born by caesarian section or induced labor. In that case, the parents get to pick the date (as long as its fairly close), and they might very well choose Feb. 29th, both because of the uniqueness of the date and the advantages of celebrating two birthdays on the same date (as my parents did with my younger brother), you only need one cake, one party, if the budget's tight they can even share one present.
And as for the unlikelihood of births 4 or 8 years apart, my sister has three sons born on three different presidential inauguration days (4 years apart, although the day of the month was different each time). [/hide]

Title: Re: Leap Year Birthdays
Post by NickH on Nov 16^th, 2003, 2:04am

Quote:

You forgot one very big factor:
The possibility one of the younger children was born by caesarian section or induced labor. In that case, the parents get to pick the date (as long as its fairly close),...

[hide]You're right -- I didn't consider that! In fact, I didn't even realise it was the case, specifically for c-section or induced labor.

How close is "fairly close"? Within a few minutes? A few hours? A few days? Only in the latter case could this factor significantly affect the estimate. And don't forget -- the option arises only if the birth date is close to February 29th, itself rare.

A related factor is: already having one child with a birthday of February 29th, would the parents deliberately aim for the next February 29th? How likely is that? And how likely is it they would succeed? Overall, I don't think this factor is as significant as that of multiple births.[/hide]

Title: Re: Leap Year Birthdays
Post by towr on Nov 16^th, 2003, 7:49am

I estimate the probability is about 0..

Title: Re: Leap Year Birthdays
Post by NickH on Nov 16^th, 2003, 8:19am

Quote:

I estimate the probability is about 0..

Why do you say that, towr?

Title: Re: Leap Year Birthdays
Post by towr on Nov 16^th, 2003, 8:43am

well, give or take 1 in a million or less, and round it to the closest percent or promille..
It's just very unlikely to happen, negligible really..

[e]wow.. google actually gives a result on the query "leap year sibling" So at least there's one pair..[/e]

Title: Re: Leap Year Birthdays
Post by NickH on Nov 16^th, 2003, 8:49am

Quote:

It's just very unlikely to happen, negligible really..

But what if... [hide]Sally is one of twins?[/hide]

Title: Re: Leap Year Birthdays
Post by towr on Nov 16^th, 2003, 8:58am

It is still very unlikely..

::[hide]about 684 per million people are born on leap years (according to the [/hide][hide]honor society of leap year day babies[/hide] (http://www.leapzine.com/hr/index.html)[hide])
Odds of twins is about 12 per thousand (in the US), so multiplying that gives roughly 8.2 per million (higher than I expected, but still quite low)[/hide]::

Title: Re: Leap Year Birthdays
Post by Kozo Morimoto on Nov 20^th, 2003, 9:17pm

And leap years don't happen every 4 years ... In 400 years there are only 97 (? from memory) leap years and not 100.

Title: Re: Leap Year Birthdays
Post by rmsgrey on Nov 22^nd, 2003, 9:42pm

on 11/16/03 at 08:58:24, towr wrote:

That calculation is only valid if the probability of Sally being twins is independent of the probability of Sally's sibling being born on a leap day. Since we're told Sally was a leap baby, the probability of her (hypothetical) twin being born on the same leap day is probably rather better than 684 per million (I'd guess around 990000 per million based on an expected gap between twin births of around 15 minutes, but since I plucked that figure out of the air, I may be a little off)

Title: Re: Leap Year Birthdays
Post by towr on Nov 23^rd, 2003, 8:14am

You're right..
So the chance is at least equal to the chance she's a twin.. But I think someone allready said that..