Binomial/Poisson (or any ) Distribution for finding out probability of me getting into a business school,plz help with my calculation.

Probability of getting into a business school is 10%,I have applied to 12 business schools,what is probability that i get accepted by atleast 1 of them?
My solution as per Binomial Distribution:-
Probability of success(p)=1/10.
Probability of failure(q)=9/10.
Number of observations(n)=12.
= 0.97176

My solution as per Poisson distribution:-
Mean Number of acceptances=1/10
Number of observations=12

(so according to above example , probability of me getting accepted in atleast one business school is 96%, is it really true,because i have onlu 10 % chance of getting accepted when i apply to only 1 school, plz explain any mistakes)