Birthday Paradox Case Study
Birthday paradox Since I will be applying the birthday paradox to solve this problem, it is necessary to first find out how the birthday paradox works. According to the birthday paradox, in a room with just 23 people, the odds of at least two people having the same birthday is 50%. The method that is preferred when solving the birthday paradox is to find the opposite of our desired value: The odds of not having two people with the same birthday. For the first person, it doesn’t matter what his birthday is, but for the second person, simply find the probability that the person does not have the same birthday as the first person; this should be the total number of possible days minus 1. When the third person enters the room, the probability of that person …show more content…
In other words, the probability of at least two people having the same birthday is 1 minus. Therefore Probability of having with same birthday = 1 – 0.493 = 0.507 = 50.7% It may seem odd for a mere number of 23 people for a 50% chance of someone sharing the same birthday, however if you look at it differently and look at the number of pairs that 23 people can make with their birthdays, the number makes much more sense. There are 365 days in a year and half of that would be 182. So at least 182 people to have 50-50 chance. Strangely enough the answer to this question is only 23 people are necessary to have a 50% chance at least two people in the group will share a birthday. This situation, where the answer is counter intuitive, is called a paradox, making the official name for this probability problem, the Birthday paradox. The question is : how many people would you need in a group for there to be a 50-50 chance that at least two people will share a
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