3. A classroom has three doors. Let NV be the total number of students who enter the classroom. Let NA be the number of students who enter through Door A, NB the number who enter through Door B, and Nc the number who enter through Door C, so that NA + NB + Nc = N. Suppose each student enters through a door picked according to the following distribution, independently of all other students and independently of the value of N. Door A Door B Door C 0.5 0.4 0.1 a) Suppose N = 20 with probability 1. Find P( NA = NB | Nc = 0). b) Suppose N has the Poisson (20) distribution. Find P( NA = NB