Abox contains 6 identically sized, solid-colored balls. one ball is green, 2 are yellow, and 3 are red. a ball is drawn at random and returned to the box, then a second ball is drawn at random. what is the probability that the first ball is red and the second ball is green?

When you draw the first ball, you have three positive outcomes (the three red balls) and 6 possible outcomes (any of the six balls in the box).

This means that the probabilty of getting a red ball in the first draw is

since you return the first drawn ball to the box, the second drawn takes place with the same conditions as the first, exept this time you're looking for a green ball, and thus you only have one positive outcome. So, the probability of getting a green ball is

The probability of two independent events occuring one after the other is the product of the two probabilities, so the answer to your question is