Renewal process

Friend and I are working on this question:

Consider a renewal process with interval density

f_X(x) = l^2 x exp(-lx),

defined for x>0. So intervals have a gamma distribution (2,l).

a. Delete every event independently with probability p. Why is this
still a renewal process? What is the new renewal density, and mean
number of surviving events in an interval of length v starting from a
surviving event?
b. Delte every interval with probability p, so that at the end of each
interval there are multiple occurrences. What is the joint
distribution of the intervals between distinct event times and their
multiplicities? What is the mean number of events (including
multiplicity) in an interval of length t from time 0?

Really, really stuck ...any help would be well appreciated!
.