Geometric Distribution

I'm trying to solve the following problem:

The number of bombs required to achieve the disintegration is assumed to be geometrically distributed. In one series in which y bombs are available, x of these bombs failed. What is the probability that it will disintegrated by the end?

My understanding & solution:

We know that the memoryless property states that: $P(X >s+t|X >t)=P(X >s)$

Now I think that the probability is: $1 - P(X>(y-x) +x | X >x)= 1 - P(X>(y-x))$

Here I have set :

• t = the number of bombs which failed => x
• s = the number of bombs available => (y-x)

Is my reasoning correct? Sorry for the lack of proper wording but this is all new to me and I'm still trying to join the dots.