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
A "passing game" follows these rules: At the nth level, a die is thrown n times. If the sum of the points from these n throws is greater than \(2^n\), the player passes the level. Questions:
(1) What is the maximum number of levels a player can pass in this game?
(2) What is the probability of passing the first three levels consecutively?
(Note: The die is a fair cube with faces showing 1, 2, 3, 4, 5, 6 points. After a throw, the number shown on the top face when the die comes to rest is the point rolled.)
user
\frac{100}{243}
rule
A "passing game" follows these rules: At the nth level, a die is thrown n times. If the sum of the points from these n throws is greater than \(2^n\), the player passes the level. Questions:
(1) What is the maximum number of levels a player can pass in this game?
(2) What is the probability of passing the first three levels consecutively?
(Note: The die is a fair cube with faces showing 1, 2, 3, 4, 5, 6 points. After a throw, the number shown on the top face when the die comes to rest is the point rolled.)
train