题目
A bag contains a large number of counters with an odd number or an even number written on each.
Odd and even numbered counters occur in the ratio 4 : 1
In a game a player takes a random sample of 4 counters from the bag.
The player scores
• 5 points for each counter taken that has an even number written on it
• 2 points for each counter taken that has an odd number written on it
The random variable X represents the total score, in points, from the 4 counters.
(a) Find the sampling distribution of X
A random sample of n sets of 4 counters is taken. The random variable Y represents the number of these n sets that have a total score of exactly 14
(b) Calculate the minimum value of n such that P(Y ≥ 1) > 0.95
(Total for Question 6 is 9 marks)
题目中文翻译
一个袋子里有大量筹码，每个筹码上写有奇数或偶数。
奇数和偶数筹码的比例为 4 : 1
在一场游戏中，玩家从袋中随机抽取 4 个筹码。
玩家得分
• 每个抽到的偶数筹码得 5 分
• 每个抽到的奇数筹码得 2 分
随机变量 X 表示 4 个筹码的总得分。
(a) 求 X 的抽样分布
随机抽取 n 组 4 个筹码。随机变量 Y 表示这 n 组中总得分恰好为 14 的组数
(b) 计算最小的 n 值，使得 P(Y ≥ 1) > 0.95
（第 6 题共 9 分）