You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
system
Five friends: Abby, Bernardo, Carl, Debra, and Eliza play a modified game where each starts with five coins. The game consists of four rounds, and in each round, five balls are placed in an urn—one green, one red, one yellow, and two white. Each player draws a ball at random without replacement. If a player draws the green ball, they give one coin to the player who draws the red ball. If a player draws the yellow ball, no coin transaction occurs for that player in that round. Determine the probability that, at the end of the fourth round, each of the players has five coins.
user
\frac{1}{81}
rule
Five friends: Abby, Bernardo, Carl, Debra, and Eliza play a modified game where each starts with five coins. The game consists of four rounds, and in each round, five balls are placed in an urn—one green, one red, one yellow, and two white. Each player draws a ball at random without replacement. If a player draws the green ball, they give one coin to the player who draws the red ball. If a player draws the yellow ball, no coin transaction occurs for that player in that round. Determine the probability that, at the end of the fourth round, each of the players has five coins.
train