Textbook Problem

$31-32$ A jar contains five red balls numbered $1$ to $5$ and seven green balls numbered $1$ to $7$.

Two balls are drawn at random from the jar. Find the following conditional probabilities.

(a) The second ball drawn is red, given that the first is red.

(b) The second ball drawn is red, given that the first is green.

(c) The second ball drawn is even-numbered, given that the first is odd numbered.

(d) The second ball drawn is even numbered, given that the first is even numbered.