You all should find this interesting. I questioned the teacher on what was wrong with my answer and he said he was holding all questions til after Christmas. So in the meantime, I asked another math teacher to explain how to do this problem to see what he would say. Here is what he wrote down for me...
Y is a binomial random variable with parameters n=5 and p=.13. So, the probability distribution of Y is given by:
P(Y=y) = (5,y)* (.13^y)* (.87^[n-y]) for y=0,1,2,3,4,5
Since we are interested in particular in the probability of receiving no tickets on exactly ONE of the days, we are interested in P(Y=1), which is given by:
P(Y=1) = (5,1) * .13 * (.87^4) = .37
Big surprise! He has the same thing I turned it. I can't wait to hear my teacher's explanation for why he keeps marking me wrong.