John has to graph a set of parabolas of the form $y = x^{2} − 4x + 2^n$ⁿ where $n$ is an integer and $0 ≤ n ≤ 6$. What is the probability that one of these parabolas, chosen at random, will have:

1. One x-intercept?

   Answer (a):

   $P\text{(one)}=\frac{1}{7}$

   What is the value of $n$?

2. Two x-intercepts?

   Answer (b):

   $P\text{(two)}=\frac{2}{7}$

   What are the values of $n$?

3. No x-intercepts?

   Answer (c):

   $P\text{(none)}=\frac{4}{7}$

   What are the values of $n$?