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In a university with 3650 students, the professor wanted to know the probability that at least...

In a university with 3650 students, the professor wanted to know the probability that at least teo students shared the same birthday. The probability will be:

Math   Statistics-And-Probability   
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Answer #1

Let's consider the case where each person has a different birthday.

The first person, they can have 365 different birthdays. The second person can only have 364 different birthdays since we want everyone to have a different birthday. The third person has only a possibility of 363 days for a birthday. This can happen then in 365 * 364 * 363 different ways.

How many different ways total with no restrictions?:

365 * 365 * 365 Each person could be born on any day of the year.

The probability then is which equals 0.9917958341152186. This is the probability that three people will have different birthdays. Therefore, the probability that at least 2 will have the SAME birthday is 1- 0.9917958341152186 = 0.008204 . This is the compliment.

Therefore there is a 0.82% chance that from three people at least 2 will have the same birthday. Now to answer the question of 3650 people. Follow the same pattern.

This will be the probability that at least 2 of the 3650 people have the same birthday. Therefore,

=1-0=100%

1-0 =1

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