Probability - part 2

Continuing the same series of thoughts as my previous post, probability can be a handful. I have decided to give it the honour of being the only topic in which I blog about twice. The reason being, I want to place emphasis on the difficulty of the material. As stated in the previous post, Professor Antosz had given the class a few sample probability activities the past few classes... they really make you to think. These examples really opened my mind to the complexity of probability!
The second example that the Professor gave still has me wondering. We have a class of roughly 30 students, depending on the day. This past Tuesday our class was full, noting the number of students, Professor Antosz reached into his pocket and pulled out a crisp $20 bill. He wanted to place a bet, with any student willing to take it, that there were at least 2 people in the class with the exact same birthday (not the same year, but the same month and day). One brave soul took the challenge. A simple aside here, I would never place a bet against a math teacher. There job is to educate people in the field of statistics, odds, and numbers. Knowing full well that we were learning about probability, and the math teacher being the one to propose the bet, I quickly shied away.
So the Professor had each student shout out the day and month that they were born. The class was only about half way through (14 - students), when we had a match - there were 2 individuals born on June 30th. The good professor just made himself a cool 20 bones.
The majority of the class was in awe at this development. The professor stated that in group of roughly 30 the odds are high that 2 of the people will have the exact same birthday. Professor Antosz did say that he has been stumped before on 2 occasions, but that he has done this trick over 25 times. Thus this probability example has been a very profitable one.
People tend to believe that because there are 365 days in the year, the odds are very small that someone will have the exact same birthday as them. When two people come the conclusion that they share the same birthday, they are always so surprised. In reality it shouldn't be that surprising,  There are statistics that show that a majority of couples get pregnant around the same time of the year, Christmas, New Years, holidays, the summer.... That being said, in a class of 30 students the odds are good that if you were to make this major with a group of people, you would show a nice profit.
Reflecting back on probability, as a teacher I would like to split the unit on probability into 2 sections. One section taught towards the beginning of the year, the other a refresher towards the end of the year. The key element that I have pulled out of my reflecting on probability is that it is that probability is not intuitive. Our instincts lead us the wrong way when deducing examples of probability. This makes it difficult for young students to grasp. Therefore, I find it essential to bring in a variety of clever problems for the students to figure out when teaching probability. I am very much looking forward to teaching probability in my own classroom someday.