Birthday Paradox

Birthday ? Kski birthday treat do bhai treat do !

The birthday paradox basically asks

Question

What is the number of people n in a room, given that the probability of two people having the same birthday is p

By Mathematical evaluation it can be said that

$$P(same)=1-P(different)$$

Meaning that If we can find the probability of people having a different birthday in a room, We can find the probability of it being the same Now we can find the probability of $P(different)$ by:

$$P(different)=\frac{364}{365}\ast \frac{363}{365}...\frac{n-1}{365}$$

We also know about the Taylor series:

$$e^x=1+x+\frac{x^2}{2!}...1+x$$

An Approximation:

$$e^x=1-x$$

Or to be precise (for this example)

$$e^{-\frac{a}{365}}=1-\frac{a}{365}$$