A fashion designer has been working with the colors green, black, and red in preparing for the coming season's fashions. The designer estimates that there is a 0.3 chance that the color green will be "in" during the coming season, a 0.2 chance that black will be among the season's colors, and a 0.15 chance that red will be popular.
Assuming that colors are chosen independently of each other for inclusion in new fashions, what is the probability that the designer will be successful with at least one of her colors?