Math AI - The Birthday Paradox“What is the probability that at least 2 people in a room of 30 random people have the same birthday? » Probability always surrounds us, from stock markets to always simple heads or tails. This very complex area of ​​mathematics can be explained in a simpler way. This is the probability of an event occurring. The probability of an event will always be between 0 and 1. The closer it is 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 several times but each time I got a very low probability. After re-reading the question for the 20th time, I finally realized my mistake. I was thinking about the likelihood of people having the same birthday as me while the question focused on the likelihood of someone in the room having the same birthday. When I finally managed to solve the question, I didn't know what purpose it could be used for, so I did more research. That's when I discovered that the birthday paradox can also be used to decipher hashing algorithms and can be used in cryptography. The square below represents the sample space (all possible results). We haven't calculated the probability yet, so let's assume that the blank represents the number of people who have the same birthday. We will call this P(sb). The gray area represents the number of people with different birthdays. We will call this P(db). The reason we use this particular formula is that 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) = 1 This in turn means: P(sb) = 1 - P...... middle of paper ... ...an integral part of life, just like private life. The use of cryptology provides mechanisms through a digital signature. This signature is inserted using a key (which only the author of the email has) while a timestamp is linked to the document. This type of cryptography is used to control access to security facilities or pay-per-view channels. This AI started when I was trying to solve a question I've been trying to solve for ages and now I realized that we don't know some amazing things. mathematics because we are very involved. The real problem with the birthday is not the question itself but it is a test of our ignorance. My research and this problem solving helped me be more objective in my thinking and understand how incredible the odds are. I really want to solve more of these types of questions and learn more about other areas of mathematics..