Problem Statement: An urn contains 12 red, 12 green balls. Two balls are drawn one after another without replacement. The probability that the second ball drawn is green given that the first ball drawn is red is?

Solution:

Step 1: Calculate the probability of drawing a red ball in the first draw

Probability of drawing a red ball in the first draw = Number of red balls / Total number of balls
= 12/24
= 1/2

Step 2: Calculate the probability of drawing a green ball in the second draw given that the first ball drawn is red

Probability of drawing a green ball in the second draw given that the first ball drawn is red = Number of green balls left / Total number of balls left
= 12/23

Step 3: Calculate the probability of drawing a green ball in the second draw and a red ball in the first draw

Probability of drawing a green ball in the second draw and a red ball in the first draw = Probability of drawing a red ball in the first draw × Probability of drawing a green ball in the second draw given that the first ball drawn is red
= (1/2) × (12/23)
= 6/23

Step 4: Calculate the probability of drawing a green ball in the second draw

Probability of drawing a green ball in the second draw = (Probability of drawing a green ball in the second draw and a red ball in the first draw) + (Probability of drawing a green ball in the second draw and a green ball in the first draw)
= (6/23) + (12/23) × (11/22)
= 18/46
= 9/23

Therefore, the probability that the second ball drawn is green given that the first ball drawn is red is 12/23 or approximately 0.52.