Sample space for a three-sector and a four-sector spinner, the distribution of the number of threes and its expected value

A game uses two fair spinners. Spinner \(A\) has three equal sectors numbered \(1\), \(2\) and \(3\). Spinner \(B\) has four equal sectors numbered \(1\), \(2\), \(3\) and \(4\). Both spinners are spun once, and each score is the number of the sector on which that spinner stops.

1. Write down[4]
   1. all the possible outcomes, writing each as an ordered pair with the score on \(A\) first,
   2. the probability that both spinners show a score of \(3\).

Let \(Y\) be the number of spinners that show a score of \(3\).

2. Copy and complete the table below, which gives the probability distribution of \(Y\).[3]

   \(y\)	\(0\)	\(1\)	\(2\)
   \(\mathrm{P}(Y=y)\)

3. Find the expected value of \(Y\).[3]