If Stanford accepts 3 transfer students per year out of 30,000 applicants in California what is the probability that out of 15,400 applicants from southern California only one or zero get in?
Because of the extreme numbers let $p=\dfrac{3}{30,000}=10^{-4}$ the probability of success for any transfer student.
The probability that one out of $N=15,400$ is accepted is ${N\choose 1}\cdot p^1\cdot(1-p)^{N-1}$
What is the probability that none out of N is accepted?
If you add those two numbers you have the answer.