Do you mean, what is the probability of landing a certain amount of heads from the 10 trials?
I got the impression the OP meant that his/her unfair coin would have to be tossed (on average) 10 times before landing on heads once (ie: the first 9 tosses are tails).
Given that what is the chance of getting of a head with a single toss of this unfair coin.
@OP: I suck at stats so I'd not know where to start