# Statistics - Mathematics

#### Pushkar1

Joined Apr 5, 2021
416
I want to understand Mathematics before developing a model for machine learning. If I'm not wrong birthday prediction system can be build using machine learning.

For examples :

If there are 10 members in a family, what are the chances that 2 member will have the same birthday?

#### Ramussons

Joined May 3, 2013
1,227
Do we ignore Leap Years?

#### Pushkar1

Joined Apr 5, 2021
416

#### Papabravo

Joined Feb 24, 2006
18,067
The way to solve that problem is to solve a related problem. What is the probability that all 10 people have different birthdays. So you have 365 choices for the first person, 364 for the second person and so on. This leads to the following finite product:

$$\cfrac{365}{365}\cdot\cfrac{364}{365}\cdot...\cfrac{356}{365}\;=\;\cfrac{365!}{365^{10}\cdot355!}\;\approx\; 0.883$$

The probability that there are at least two people with the same birthday is 1 minus the number above. It will be about 0.117

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