### Facebook Birthdays: Virtual is the New Real

Image from Flickr

Virtual is the new real. How else would we know what really happens to our neighbors if not for Facebook? Karen, who just had her third baby and is chronically sleep deprived, entangled in her sheets and fell out of bed at night. But no worry - bruises only. Irina's husband is snoring and she is wondering what she can get him for Father's Day to ease her nights. Rich and Linda just found a snake in the back yard and killed it. Stephanie is thrilled that she is managing to breastfeed and poop at the same time, or maybe it was her older toddler that was pooping while she was breastfeeding in the same bathroom. You see, these are things that my neighbors would never discuss with me in person. They may mention the other events - renovations, vacations, work, but not these humble but honest and meaningful life moments.

Most of my neighbors would not announce their anniversaries or birthdays when meeting each other in person, but thanks to Facebook, we know who is celebrating what, in what outfit, what they are eating and whether they will be having a hangover the next day. The angels of Facebook created a gentle birthday reminder app that shows a little present icon and a name of those from your Facebook friends who are having a birthday today or tomorrow, or the day after tomorrow. If you want to show that you care, you can politely note "Happy Birthday!" and skip the rest of the wishes.

My neighbor (same person who fell out of bed) and who has 532 friends on Facebook sent me a message (on Facebook, of course). She asked whether with so many friends it is guaranteed that on any given day she may open Facebook, she'll see such friends' birthday notifications.

What do you think?
The Math Mom title comes with responsibilities...
Sometimes it is easier to solve questions that start with "What are the chances that something happens" by looking into the opposite scenario: "How likely is it that something does NOT happen." Especially if there are a lot of people that are involved in this "something". Like 532.

So, the chances that on a given day you will have a birthday notification are:

1 - (chance that NO ONE has a birthday on this day or next day or day after)

this will be:

1 - (Laura does not have birthday today-and-next-two-days AND Daniel does not have birthday today-and-next-two-days AND Caroline does not have birthday today-and-next-two-days AND continue with all your 532 friends)

(We assume here the default setting when Facebook starts notifying about a birthday two days in advance, but you can configure this and then adjust the formulas correspondingly.)

For any of your friends (Laura, Daniel, Caroline etc) the chances of not having birthday on any one specific day are (365-1)/365=364/365 as there are 365 days in a non-leap year.
The chances of not having a birthday notification today, tomorrow or day after tomorrow are (365-3)/365=362/365.
We assume that birthdays are uniformly distributed throughout the year, that is not exactly true but good enough for a large sample of Facebook users from all around the globe.

So, we will have:

1 - (362/365 AND 362/365 AND .... ), with 362/365 repeated 532 times for all the friends

when you compute the chances of two independent events happening together (A AND B) you multiply the probability of one event by the probability of the other: A x B

Therefore, we will get: 1 - (362/365 )532

this will be:

1- 0.012 = 0.9876= 98.76%

This means that there is almost 99% probability or 99 out of 100 chance that my neighbor will see a birthday icon on any given day she opens Facebook. Sounds like she may need another application to send those daily "Happy Birthday" messages.

But if you are not so popular, and have only 50 real Facebook friends, you may skip the birthday corner. The chances of seeing the icon are only 34%:

1 - (362/365) 50=
1 - 0.66 = 0.34 = 34%

So, let's not be afraid to get relaxed, open, and honest in our real virtual worlds. We'll see ourselves surrounded with friends and likely to be celebrating birthdays daily.

Cartoon by Peter Mesnik from Beyond The Gate

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