You go to a party which has 1000 guests (including you).
a) What is the probability that exactly one other guest has the same birthday as you?
b) What is the probability that at least two other guests have the same birthday as you?
My proposed solutions:
a) $(\frac{1}{365})\binom{999}1(\frac{364}{365})^{998} = 0.1771$
b) Probability of zero guests or one guest NOT having the same birthday.
Zero guests: $(\frac{364}{365})^{999} = 0.0645$
One guest: $0.1771$ (part a)
At least two guests: $1 - (0.1771 + 0.0645) = 0.7584$
Would this be the correct way to go about it?