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Another family birthday probability question

 
 
Catf
 
Reply Sat 30 May, 2015 02:02 pm
OK so my husband and I share a birthday - people are always surprised. Of course they shouldn't be. I remember being struck by the thought during a bored moment in primary school and being terribly dissapointed a moment later when I realised that the odds were approximately 365:1 - so it is likely that I know other people in the same boat.

However, we have palindromic birthdays once a decade - when I was 25, he was 52 (I know, scandellous), when I was 36 he was 63 and when I am 47 he will be 74. At first, I thought this was just a function of being born more than 11 years apart, but is isn't is it?

Furthermore, this year we have reciprocal birthdays. That is, I will be 44 because I was born in 1971 and he will be 71 because he was born in 1944.

So my question is, are these events as common as the shared birthday and I'm just failing to see the pattern or are we reallly one in a million?
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jespah
 
  2  
Reply Sat 30 May, 2015 06:10 pm
@Catf,
It's more common than you probably think, and the odds are not necessarily exactly 365:1. Some dates are just a lot more likely for births.

If you were born in September or July, those are very common months to be born in.
Most common birth dates.

http://i.dailymail.co.uk/i/pix/2013/06/09/article-0-1A3809BA000005DC-418_634x919.jpg
engineer
 
  1  
Reply Sat 30 May, 2015 08:37 pm
@Catf,
Any couple whose birthdays are a multiple of nine apart will experience the same situation as you do. Example, if a couple got married at 25 and 34 (nine apart), then they will reach 34 and 43 and every eleven years after than will have the same situation. Of course not many couples are a multiple of 9 apart in years so you are probably pretty rare.

To make the "reciprocal" thing happen, you have to have birthdays that are over 100 and the last two digits match the current year. The sum of your birthdays is 115 and this 2015 so this works for you but any couple with birthdays that add up to 115 will see the same thing this year.
markr
 
  1  
Reply Sun 31 May, 2015 09:20 pm
@engineer,
The birthday sum need not exceed 100 (born in 1920 and 1930, they will be 30 and 20 in 1950), but they do need to be born in the same century if sticking to just two digits.
Catf
 
  1  
Reply Tue 2 Jun, 2015 01:11 pm
@engineer,
Multiples of 9, of course. I'm an idiot!

Thanks engineer
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Catf
 
  1  
Reply Tue 2 Jun, 2015 01:14 pm
@markr,
Thanks Mark, very clear - most likely in the first half of a century then.
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Catf
 
  1  
Reply Tue 2 Jun, 2015 01:14 pm
@jespah,
Cheers Jespah, yup one of the darkest July days!
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