Answer:
0.3486 or 34.86%
Step-by-step explanation:
For each guest, the probability that they share a birthday with you is 1 in 365. Aside from you, there are 499 guests.
Therefore, this problem can be modeled by a binomial probability model with probability of success 1/365.
The probability of exactly 1 success in 499 trials is given by:
[tex]P(x=1) = \frac{499!}{(499-1)!}*{\frac{1}{365}} ^1*{\frac{364}{365}} ^{498}\\P(x=1) =0.3486 = 34.86\%[/tex]
There is a 0.3486 or 34.86% chance that exactly one other guest has the same birthday as you.
