An encryption algorithm generates a seed value \(z\) in the following way:

• A binary operator is chosen at random from \(\{+,\,\cdot\}\);

• Two distinct numbers \(x\) and \(y\) are chosen at random from the set \(\{1,\,2,\,...,\,9\}\) and the binary operation chosen above acts on \(x\) and \(y\) to produce \(z\).

1. What is the probability that \(z\) is an even number?
2. You notice that the algorithm generates an even \(z\) value. Given this, what is the probability that the \(+\) operator was used to generate it?