There is a 50% chance that at least two of the people in the group will share a birthday. Many people were surprised by the answer. What is it that this can be done?
When thinking about the "birthday problem" or the "birthday paradoxes" in statistics, many people think that 183 is half of all possible birthdays. Intuition doesn't fare well at this type of problem.
Jim Frost is a regular columnist for the American Society and has written three books about statistics. They show how mathematics can help us. The counterintuitive results of these problems are fun.
The answer to the birthday problem was calculated using a few assumptions. Leap years simplify the math and don't change the results. All birthdays have an equal chance of happening, according to him.
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There is a chance that the first person in the group doesn't have a birthday with the second. The chance of them sharing a birthday is about 0.21%.
The first two people cover two dates. There is a chance that the third person doesn't have a birthday with the other two. The likelihood of them all sharing a birthday is 1 minus the product of 364/365 times.
At least a pair of people will share a birthday if the number of people in a group is high. There is a 50.71% chance of that happening with 23 people. There is a chance with 57 people.
College professors will make a wager about two people sharing a birthday in a statistics class. He knows that he is almost certain to win. The students always lose on the bet. He taught them how to solve the birthday problem after he returned the money.
The answer to the birthday problem might be counterintuitive. One of the reasons that people calculate what the chances are that someone else in a group has their birthday is because of the question of whether anyone in a group shares a birthday.
About 182 people are needed for a 50% chance, because there are a lot of days in a year. They underestimate how quickly the probability increases with large groups. Group size increases the number of possible combinations. Humans don't understand exponential growth.
The birthday problem is related to a bigger problem. In exchange for some service, you're offered to be paid 1 cent on the first day, 2 cents on the second day, 4 cents on the third, 8 cents, 16 cents, and so on, for 30 days. Is that a great deal? You will have a total of $10.7 million on the 30th day, even though most people think it's a bad deal.
It was originally published on Live Science
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