In a class of 72 students at least two will share a birthday
There is a problem in mathematics relating to birthdays. Since a year has 366 days (if you count February 29), there would have to be 367 people gathered together to be absolutely certain that two of them have the same birthday. Now, if we were content to be just fifty percent sure, how many people are needed to be in the room? A good guess might be 183 since that is half of 366. The surprising answer is that there need only be 23 people present! Stated differently, half of the time that twenty-three randomly selected people are gathered together, two or more of them will share the same birthday (an explanation is given in my letter below). This is a delightful activity to do with students in your classroom. If your class size is 23 or more, you have at least a 50% chance that two students will share a birthday. The Problem: In a group of n people, what is the probability that two of them will have the same birthday? Show
Here is a letter that I wrote to Marilyn vos Savant about the Birthday Problem in Statistics (She published an edited version of this letter in November 1997 in her column in Parade magazine):
Here is Marilyn vos Savant's column from the November 23, 1997 PARADE magazine:
What is the probability that at least 2 people share the same birthday?What's the chance that two people share the same birthday? The first person can be born on any day of the year, this means that the probability is 365/365 = 1. The second person has to be born on the same day as the first and there is a 1/365 chance of that happening.
What is the probability that at least 2 people have the same birthday in a group of 20 people?If there are 366 or more people, but only 365 possible birthdays disregarding leap year, then two or more of them must share a birthday.
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Probability of Shared Birthdays. or, How to Win Money in Bar Bets.. How do you solve the birthday paradox?By assessing the probabilities, the answer to the Birthday Problem is that you need a group of 23 people to have a 50.73% chance of people sharing a birthday! Most people don't expect the group to be that small. Also, notice on the chart that a group of 57 has a probability of 0.99. It's virtually guaranteed!
Is the birthday paradox true?The birthday paradox is strange, counter-intuitive, and completely true. It's only a “paradox” because our brains can't handle the compounding power of exponents. We expect probabilities to be linear and only consider the scenarios we're involved in.
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