A chain of video stores sells three different brands of DVD players. Of its DVD player sales, 50% are brand 1 (the least expensive), 30% are brand 2, and 20% are brand 3. Each manufacturer offers a 1-year warranty on parts and labor. It is known that 25% of brand 1's DVD players require warranty repair work, whereas the corresponding percentages for brands 2 and 3 are 20% and 10%, respectively. Create a tree diagram and find the probability that a randomly selected purchaser has a DVD player that is brand 1 given they needed a repair under the warranty. To receive full credit, you must completely fill out all levels of the tree diagram with all probabilities listed.