Count tries when keys are tested without replacement

John has four keys, only one of which unlocks a door. He tries the keys randomly without replacement. X is the number of tries needed to unlock the door.

(i) Show that $P(X=3)=1/4$.

(ii) Tabulate the distribution of X.

(iii) Write down $E(X)$ and $\operatorname{Var}(X)$.

(iv) Find $P(X^2<8)$.