Thursday, November 27, 2014

Our special day

November 27 is our very Special day. Not because it's Thanksgiving this year, although that is very nice. It's because four of our sisters share November 27 as their birthday! Happy birthday Karen, Colette, Beth and Ann.

Now, this brings to mind the rather well-known mathematics fact: There is a high probability that in a room of 30 people, that two will share the same birthday. In fact, the probability of that happening is just over 70%.

I am feeling very cocky today and so I am going to try and show you why this is true! Here goes..last chance to get out of this page. I won't blame you......Have a nice holiday.

For those who stayed: the idea here is that it's easier to compute the probability of NOT sharing a birthday and then, subtract that answer from 1 (100%) to get the chances OF sharing, because sharing or not sharing together make up 100% of all that can happen.

We'll start with 30 people. The first person has a certain birthday. What are the chances that the 2nd person will NOT share that date (have her own unique birthday)? The chances are 364/365, because there are 364 days available, not taken by the first person. Now a 3rd person comes along and what is his chance of NOT sharing one of the first two's birthday dates? 363/365, because two days are taken by the first two people, leaving 363 free.

How are you doing with this logic?!

Now, we continue this string of fractions for all 30 people. By the way, the last person's chances of NOT sharing a date already taken as a birthday by any of the other 29 is the fraction 336/365.

Now in probability when you want things ALL to happen in one situation, you must multiply their individual chances. We would multiply all the fractions---all of which have a denominator of 365 by the way. It's a mess, but a calculator or computer does it easily.

When you do this, you get the answer, in decimal form, 0.294 In percentage form that is 29.4% Now here comes the grand finale: Ta Da! Remember all of these were chances that they WOULD NOT share a birthday, so if any two DID share a birthday, it would be 100% - 29.4% or 70.6% chance that at least two WILL INDEED share a day.

This is truly amazing, because when you realize that you'd really have to have 366 people to be 100% sure that two would share a birthday (Hint: the first 365 could all have separate birthdays, couldn't they? But the 366th person would have to double up with someone!)

Now, if you've survived this far I hope you realize that you are much smarter in Math than some bad experience in math class in some grade made you think!! And the next question in your head is probably, In a community of 101 women, what are the chances that four share the same birthday? And the answer is, I'm nowhere near smart enough to even set it up, let alone do it! Suffice is to say that we have such and it's loads and loads of fun....which is what I hope you had a little of here.

Happy Thanksgiving and Blessed Advent, which begins this weekend, too.