{"status": "success", "data": {"description_md": "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.\n\nApples 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 $10000P$.", "description_html": "<p>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. <span class=\"katex--inline\">50\\%</span> of the trees in the orchard produce one of the red apple species, and <span class=\"katex--inline\">20\\%</span> produce the other red species.</p>&#10;<p>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 <span class=\"katex--inline\">P</span> be the probability they get at least two red apples. Find the value of <span class=\"katex--inline\">10000P</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "TxO Math Bowl 2024 - Guts Contest - Set 6 Problem 2", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}