Long two before you sell one

You are making a market and quoting both sides. Your bid is hit as a Poisson process at rate 6 per hour, and your offer is lifted, independently, as a Poisson process at rate 4 per hour. Each fill is for one unit, and you start flat.

(a) What is the probability that your bid is hit at least twice before your offer is lifted for the first time?

(b) What is the expected number of bid fills before the first offer fill?

(c) What is the expected time until your first fill of either kind?