Letter cards drawn one after another without replacement: a first-draw probability, a conditional probability and a joint probability

Each letter of the word \(\mathrm{PROBABILITY}\) is written on its own card, giving \(11\) cards: \(\mathrm{P, R, O, B, A, B, I, L, I, T, Y}\). Two cards are taken at random, one after the other, and the first card is not put back. The event \(A\) is that the first card taken shows the letter \(\mathrm{A}\), and the event \(B\) is that the second card taken shows the letter \(\mathrm{B}\).

1. Find \(\mathrm{P}(A)\).[1]
2. Find \(\mathrm{P}(B\mid A)\).[2]
3. Find \(\mathrm{P}(A\cap B)\).[3]