Final answer:
The total number of balls in the basket is 36, calculated from the 12 red balls and their 1 in 3 selection probability. Dividing the total by the 1 in 4 probability for the green balls gives us 9 green balls.
Step-by-step explanation:
The question asks us to determine how many green balls are in a basket, given that the probability of randomly choosing a red ball is 1 in 3, and there are 12 red balls in total. The probability of selecting a green ball is 1 in 4. To find out how many green balls are in the basket, we need to establish the total number of balls in the basket based on the probability of picking a red ball.
Since the probability of choosing a red ball is 1 in 3, for every red ball there should be two more of other colors, making the total 3 balls for every single red ball. This means the total number of balls in the basket should be 3 times the number of red balls, which is 3 * 12 = 36 balls. Now, to find the number of green balls, we can use the fact that the probability of choosing a green ball is 1 in 4. Since the total number of balls is 36, we divide this number by 4, giving us 36 / 4 = 9 green balls.
The correct answer to the question is therefore C. 9 green balls.