Death Process using R Software

If anyone can help me you are a genius (in my book anyway!)

R-Software is a downsized version of the famous S-plus software.
I was wondering if someone could help me with the following...

If a population starts at time 0 with 4 individuals and follows a pure death process at a rate of 1 every 2 days.

i) Find the probability that there is exactly one individual alive after a week?

I know the answer is 0.1102.

But I can't understand why.
I have tried all possible configurations of dnbinom and nothing seems to work.