When I decided to become a math major in college, I knew that to complete this degree, in addition to the required calculations, there were two - advanced calculus - probability theory and mathematics 52, which were statistics. Although Prospect was a course I was looking forward to, given my penchant for games and games of chance, I quickly discovered that this theoretical mathematics course was not a walk in the park. Despite this, it was in this course that I learned about the birthday paradox and the mathematics behind it. Yes, at least two shared common birthdays in a room of about twenty-five people are better than 50-50. Read on and see why.
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The birthday paradox must be one of the most well-known and well-known problems in probability. In For example, do you ever remember talking casually with someone you met at a party and discovering that his brother had the same birthday as your sister? In fact, after reading this article, if you create a mindset for this event, you will start to notice that the birthday paradox is more common than you think.
Because there are 365 possible days on which a birthday can fall, it seems unlikely that a birthday of two people in a room of twenty-five people should be a common birthday. And yet this is completely the case. remember. The key is that we are not saying which two people will have the same birthday, just that some will have the same date in their hands. The way I will make it come true is by examining the mathematics behind the scenes. The beauty of this explanation would be that you would not need more than a basic understanding of arithmetic to understand the import of this paradox. That's right. You will not have to master combustible analysis, permutation theory, complementary probability spaces - none of them! You just have to put on your hat of thought and take this quick ride with you. let's go.
To understand the birthday paradox, we will first look at the simplified version of the problem. Let's look at examples with three different people and ask if there is a possibility that they will have a common birthday. Many times the problem in the problem is solved by looking at the problem. By this, we mean quite simple. In this example, the given problem is likely that the birthdays of two of them are common. The complementary problem is the possibility that no one's birthday is normal. Either his birthday is common or not; These are only two possibilities and thus this is the approach to solve our problem. This corresponds perfectly to the situation in which a person has two choices, either A or B. If they choose A they did not choose B and vice versa.
In a birthday problem with three people, A likes or is likely to have a common birthday of two. In probability problems, the results that an experiment performs are called probability sampling locations. To make this crystal clear, take a bag with 10 balls numbered 1–10. The probability space consists of 10 numbered balls. The probability of the entire space is always equal to one, and the probability of any event that forms part of the space will always be less than or equal to one fraction. For example, in the scenario of a numbered ball, if you reach into the bag and take out one, the probability of picking any ball is 10/10 or 1; However, the probability of choosing a specific numbered ball is 1/10. Look at the distinction carefully.
Now if I want to know the probability of choosing the number 1 ball, I can calculate 1/10, because only one ball is number 1; Or I can say that the probability is a minus in which there is a possibility of not picking the numbered ball. 1. Not selecting the ball is 19/10, because there are nine other balls, and
1 - 9/10 = 1/10. In any case, I get the same answer. It is the same approach - with slightly different mathematics - that we will take to demonstrate the validity of the birthday paradox.
In the case of three people, observe that each person can be born on any one of the 365 days of the year (for the birthday problem, we neglect the leap year to simplify the problem). To get the denominator of the numerator, the probability space, to calculate the final answer, we assume that the first person can be born on any of the 365 days, the second person in the same way, and the third person. So the number of possibilities would be 365 times the product of 365 or 365x365x365. Now, as we mentioned earlier, to calculate the probability that at least two have a normal birthday, we will calculate the probability that no two have a normal birthday and then subtract it 1. Remember A Or any one of B and A = 1-B, where A and B represent the two events in question: In this case, the probability of A is that at least two have a normal birthday and B represents this probability. That they both have no normal birthday.
Now for a couple to not have a normal birthday, we should find a number of ways. By the way, the first person can be born in any of the 365 days of the year. In order for the second person not to match the first person's birthday, this person must be born on either of the remaining 364 days. Similarly, for the third person not to share the birthday with the first two, then this person must be born on either of the remaining 363 days (which we subtract two days for persons 1 and 2). Thus the probability of two out of three people having a common birthday would be (365x364x363) / (365x365x365) = 0.992. Thus it is almost certain that no one in the group of three will share a shared birthday with the others. The probability that two or more common birthdays will be 1 - 0.992 or 0.008. In other words, less than 1 in 100 shots means that two or more would have a common birthday.
Now things change to a great extent when the size of the people we believe gets up to 25. Using the same arithmetic and the same arithmetic with three people, we have 365x365x the total possible birthday combinations in a room of 25. .. x365 twenty-five times. One of the ways in which no two can share is his birthday 365x364x363x ... x341. The quotient of these two numbers is 0.43 and 1 - 0.43 = 0.57. In other words, in a room of twenty-five people, there is a better than 50–50 chance that at least two will have a similar birthday. Interesting, no? Amazing what mathematics and especially what probability theory can show.
So for those of you who have a birthday today as you are reading this article, or are celebrating a birthday soon. And as your friends and family gather around your cake to make your birthday happy, be happy and joyful that you've made another year - and don't forget the birthday paradox. Isn't life grand?
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