Conditional Probability with Marbles

A researcher conducts an experiment to understand the distribution of outcomes in a series of independent trials. She has a bag containing 10 marbles: 4 red, 3 blue, and 3 green. Each trial consists of drawing one marble at random, noting its color, and then replacing it in the bag before the next draw.

Assume that the researcher will draw marbles from the bag 5 times, with each draw being independent of the others. Let event A be that at least one red marble is drawn and event B be that at least one green marble is drawn. What is the probability that event A occurs given that event B has occurred?