A darts player practises throwing a dart at the bull's eye on a dart board. Independently for each throw, her probability of hitting the bull's eye is 0.2. Let X be the number of throws she makes, up to and including her first success.

(a) Find the probability that she is successful for the first time on the third throw.

(b) Write down the distribution of X and give the name of the distribution.

(c) Write down the probability that she will have at least three failures before her first success.