Consider a random collection of n individuals. When approximating the probability that no 3 of these individuals share the same birthday, a better Poisson approximation than that obtained in the text (at least for values of n between 80 and 90) is obtained by letting $E_i$ be the event that there are at least 3 birthdays on day i, i=1,......,365.
(a) Find P($E_i$).
(b) Give an approximation for the probability that no three individuals share the same birthday.
(c) Evaluate the preceding when n=88 (which can beshown to be the smallest value of n for which theprobability exceeds 0.5).
Any help is greatly appreciated!
Hint : The poisson-distribution is a well approximation of the binomial distribution, if $n$ is large and $p$ is small. The parameter $\lambda$ is $\lambda=np$ in the approximation.