Determine $P(X > n +k\mid X > n)$ 
Bob is at the shooting range. 
  With probability $\frac{1}{3}$ Bob hits the target. 
  Every shot is independent of the previous ones. 
  Bob starts and keeps shooting until he hits the target. 
  Let the random variable $X$ be the number of the shot that first hits the target. 
  For integers $n$ and $k$, determine $P(X > n +k\mid X > n)$.

I start working on the conditional probability that becomes: $P(X > n +k\mid X > n)=\frac{P(X > n + k\:\cap\:X > n)}{P(X > n)}=\frac{P(X > n+ k)}{P(X > n)}$ 
Now how can I compute the probabilities from the data that I know, which distribution should I use, or how can I use the probabilities given in the question?
 A: The way I understand this is:
What's the probability that it will take at least n+k shots to git the target given that it will take  at least n shots?
So I imagine this scenario:
Bob already took n shots (and missed), what's the probability that he'll have to take at least k more shots before he hits the target?
Note the condition given: Every shot is independent of the previous ones. 
So to me it is clear that it doesn't matter that Bob already took n shots and missed. The chances he'll need k more shots now is the same as if he had just now started trying. In other words:
P(X > n + k | X > n) = P(X > k)
A: The probability of Bob not hitting the target is $2/3$, so the probability that he misses $x$ times is $(2/3)^x$, since the individual shots are independent. How could you express the statement "Bob misses the target $n$ times" symbolically?
A: Hint:
Observe that event $\{X>m\}$ is the same as the event that the first $m$ attempts did not succeed. 
Find the probability of this event for $m=n$ and for $m=n+k$.
Google on "geometric distribution".
