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
During the Spring Festival, a supermarket holds a promotional lottery event. When the amount spent by a customer reaches a certain threshold, they can participate in a lottery. The rules of the event are: from a box containing 3 black balls, 2 red balls, and 1 white ball (identical except for color), customers can draw balls.
(Ⅰ) If the customer spends more than 100 yuan but no more than 500 yuan, they can draw 2 balls at once. Each black ball drawn is rewarded with 1 yuan in cash, each red ball is rewarded with 2 yuan in cash, and each white ball is rewarded with 3 yuan in cash. Calculate the probability that the total reward money is at least 4 yuan.
(Ⅱ) If the purchase amount exceeds 500 yuan, they can draw twice from the box, drawing one ball each time and then returning it before drawing again. Each black ball and white ball drawn is rewarded with 5 yuan in cash, and each red ball is rewarded with 10 yuan in cash. Calculate the probability that the total reward money is less than 20 yuan.
user
\frac{8}{9}
rule
During the Spring Festival, a supermarket holds a promotional lottery event. When the amount spent by a customer reaches a certain threshold, they can participate in a lottery. The rules of the event are: from a box containing 3 black balls, 2 red balls, and 1 white ball (identical except for color), customers can draw balls.
(Ⅰ) If the customer spends more than 100 yuan but no more than 500 yuan, they can draw 2 balls at once. Each black ball drawn is rewarded with 1 yuan in cash, each red ball is rewarded with 2 yuan in cash, and each white ball is rewarded with 3 yuan in cash. Calculate the probability that the total reward money is at least 4 yuan.
(Ⅱ) If the purchase amount exceeds 500 yuan, they can draw twice from the box, drawing one ball each time and then returning it before drawing again. Each black ball and white ball drawn is rewarded with 5 yuan in cash, and each red ball is rewarded with 10 yuan in cash. Calculate the probability that the total reward money is less than 20 yuan.
train