TxO Math Bowl 2024 - Guts Contest - Set 6 Problem 2

An apple orchard has several types of apple trees, specifically: two different red species, and one green species. Every tree in the orchard must produce one and only one of these 3 types of apples. 50\% of the trees in the orchard produce one of the red apple species, and 20\% produce the other red species. Apples of the same colour are indistinguishable and there are always enough apples on each tree for them to pick from. If someone were to pick a tree three times, and pick one apple from the tree each time it was chosen, let P be the probability they get at least two red apples. Find the value of 10000P.