#analysis/probability-statistics Say we assemble 50 random people. What is the probability that some two share birthdays of same day & month? What is the [[sample space]]? Suppose that 50 people walk in and one-by-one declare their days. Allowing for leap years, the - 1st person has 366 choices - 2nd person has 366 choices - $\vdots$ - 50th person has 366 choices By the [[multiplication principle]] we have $\vert \Omega \vert = 366^{50}$. It's easier to analyze the complement— what is the probability that no two share a day? This means that as our people enter the room, we would have - 1st person has 366 choices - 2nd person has 365 choices - $\vdots$ - 50th person has 366-50+1=317 choices Thus $\vert A^c \vert = \frac{366!}{317!}$ and $P(A^c) = \frac{\vert A^c \vert}{\vert \Omega \vert} \approx 0.03$ So its 97% probable that two share a birthday! #notFormatted