RESPOND TO THESE COMMENTS BY EXPRESSING OPINION AND SUGGESTION.

1)Birthday Paradox or Birthday Pairs

A birthday paradox is humans unfortunate intuition getting in the way of understanding how math works around us on a daily basis. As a child, I struggled to believe that anyone shared my birthday with me. Now to be clear, I am not sure that we are looking at year just date. This being said, it still seems like a big shock to our systems when we find someone else with our birthday. As I aged, I outgrew some of the shock and amazement at this when I went searching for famous people who shared my birthday and began analyzing who I knew with the same birthday or close by. For instance, my mom and her best childhood friend were born on the same day in the same year. That is probably a little less likely, but my son and a close family friend's daughter were also born on the same day in the same year. My youngest son shared a birthday with two of my previous students, and my brother shares a birthday with Abraham Lincoln. These are the facts that I grew up with, so a little less of a shock of the birthday paradox as I dreamed of meeting someone who shared my birthday so that we could party together. I got close with my best friend who was born on July 4 and my college roommate that was born on June 23, my birthday being the 22 of June. It may not be typical or at least we do not think it is typical, but according to the definition of unusual (less than 5%) the birthday paradox is a usual or accepted probability.

With 23% giving us a probability of 50.73% and only 70% giving us a 99.99% probability of a shared birthday, it should become a standard we recognize. Unfortunately, many non mathematicians, like myself, do not understand how this could be possible. Our brains do not understand nonlinear functions such as pairings. There is a math set called combinatorics that specializes in checking how many ways any given thing can be recognized. This is most likely based on probability. It starts with calculating all of the ways that something could not happen, such as the birthday paradox. Then subtracting that from 100 gives then the stats on how often it could occur. This is similar to computing probabilities complements after computing time lapsed permutations.

I don't agree that everyone is caught in birthday paradox, but every individual is also raised differently. I grew up with family who sought to teach us who we shared out day with and how that person was important. I also grew up in a home with a tool and die maker who lived for probabilities and mathematics defining everything.

2)The "Birthday Problem" discusses how big a group of people would have to be in order for there to be at least a 50% chance that two people within the group have the same birthday. Typically 23 people are needed within a group to have a 50% chance of a duplicate birthday. The best way of finding the probability of a match of birthdays is to calculate the odds that the everyone's birthday is different. This is calculated by subtracting the probability of no match from 100 to find the probability of a match. Typically 75 people are needed within a group to have a 99% chance of a duplicate birthday. I do know two people with the same birthday and I find this unusual and seemingly very odd. In this class unusual is defined as data more than two standard deviations away from the mean in either direction.