Unknown probabilities and expected scores of two biased spinners and a game comparing their scores

A biased spinner, \(A\), has four sectors with scores \(1\), \(2\), \(3\) and \(4\). The random variable \(X\) is the score when \(A\) is spun once, and its probability distribution is given in the table.

1. Find \(p\).[2]
2. Hence, find \(\mathrm{E}(X)\).[2]

A second biased spinner, \(B\), also has sectors with scores \(1\) to \(4\). The random variable \(Y\) is the score when \(B\) is spun once, with the probability distribution below.

3. 1. Write down the interval of possible values of \(r\).
   2. Hence, deduce the interval of possible values of \(q\).[3]
4. Express \(\mathrm{E}(Y)\) in terms of \(r\), and hence find the interval of possible values of \(\mathrm{E}(Y)\).[3]

In a game, spinners \(A\) and \(B\) are each spun once, independently. The probability that the score on \(A\) is lower than the score on \(B\) is \(\dfrac35\).

5. Find \(\mathrm{E}(Y)\).[6]