Math IA - The Birthday Paradox“What is the probability that at least 2 people in a room of 30 random people have the same birthday?”Probability is always around us, from stock markets always simple heads or tails. This very complicated area of ​​mathematics can be explained more simply. It is the probability that an event will happen. The probability of an event occurring will always be between 0 and 1. The closer to one, the more likely the event is to occur. I chose this topic because when I first read the birthday problem in the textbook, I tried to solve it repeatedly but every time I would get a very low probability. After rereading the question for the twentieth time, I finally realized my mistake. I was considering the probability of people having the same birthday as me when the question focused on the probability of someone in the room having the same birthday as me. When I finally got around to solving the question, I didn't know what else it could be used for, so I did more research. That's when I discovered that the birthday paradox can also be used to crack hashing algorithms and can be used in cryptography. The square below represents the sample space (all possible outcomes). We haven't calculated the probability yet, so let's assume that white represents the number of people celebrating the same birthday. We will call it P(sb). The gray area represents the number of people who have different birthdays. We'll call it P(db). The reason we use this formula in particular is because the birthdays of 30 random people in a room are all independent events that do not depend on each other for their occurrence. Since the maximum probability of an event is 1 this means:P(db) + P(sb) = 1This in turn means:P(sb) = 1 - P...... half of the paper..... .that part of life just like privacy. The use of cryptography provides mechanisms through a digital signature. This signature is inserted via a key (which only the person writing the email has) while a timestamp is associated with the document. This type of encryption is used to control access to security installations or pay-per-view television channels. This AI started with me trying to solve a question I had been trying to solve for years and now I realized that we ignore some amazing math because we are so self-involved. The real problem with the birthday is not the question itself but it is proof of our ignorance. My research and problem solving have helped me be more objective with my thinking and understand how amazing probability really is. I definitely want to solve more of these types of questions and learn more about other fields of mathematics.