This exercise is about conditional probability, but I am stuck

A jar contains eight red balls numbered 1 to 8, and five green balls numbered 1 to 5. Two balls are drawn at random from the jar. Find the following conditional probabilities. (Enter your probabilities as fractions.)
(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.

Question

This exercise is about conditional probability, but I am stuck

A jar contains eight red balls numbered 1 to 8, and five green balls numbered 1 to 5. Two balls are drawn at random from the jar. Find the following conditional probabilities. (Enter your probabilities as fractions.)
(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.

queelius · Answer

(a) P[red_2 | red_1] = #(red balls remaining) / #(balls) = (8-1)/(8+5-1)

The remaining questions can be answered in a similar way.

anonymous · Answer

@queelius I tried the same formula and attempted to answer it 4 times online and got it completely wrong :( Im dumb