I was asked this: the number of electrons coming out of a device during 1 hour is a random Poisson variable with $\lambda = 4$. Electrons coming out of the device hit a wall with a probability of $\frac{3}{4}$ independently. What is the probability that from the electrons that came out of the device during 1 hour:  

1) at least 1 hit the wall?  

2) exactly 3 hit the wall?

So at first I calculated the probability that at least 1 electron came out of the device during 1 hour and got $1 - \frac{1}{e^4}$ and then:

for (1), I said if $k$ is the number of electrons that came out during 1 hour then my answer is $(1 - \frac{1}{e^4}) \cdot {k \choose 1} \cdot \frac{3}{4}$   

I took the probability that at least one electron came out and then chose 1 from the $k$ that came out and then multiplied by the probability that they hit the wall.

for (2) I did a similar thing but I took the probability that at least 3 came out during 1 hour, then choose 3 from the $k$ electrons that came out, and then multiplied by $(3/4)^3\cdot(1/4)^{k-3}$

But I think I'm not even doing this right. Can I get some help here?