题目
Bag contains 6 red marbles, 5 blue marbles and 1 green marble.
Bag contains 5 red marbles and 3 blue marbles.
A marble is chosen at random from bag and placed in bag .
A marble is now chosen at random from bag .
(a) Draw a tree diagram to represent this information, giving the probability on each branch.
(b) Find the probability that both marbles chosen are the same colour.
(c) Find the probability that the marble chosen from bag is blue, given that the marble chosen from bag is blue.
题目中文翻译
袋 中有 6 颗红色弹珠、5 颗蓝色弹珠和 1 颗绿色弹珠。
袋 中有 5 颗红色弹珠和 3 颗蓝色弹珠。
从袋 中随机选取一颗弹珠，放入袋 中。
现在从袋 中随机选取一颗弹珠。
(a) 画出树状图来表示这些信息，并标出每条分支上的概率。
(b) 求所选两颗弹珠颜色相同的概率。
(c) 已知从袋 中选出的弹珠是蓝色的，求从袋 中选出的弹珠是蓝色的概率。
原卷通用作答要求
Answer all questions. You should use a calculator where appropriate.
You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。
解答
(a)
解法一
思路
展开
先从A取出的颜色决定B增加哪种颜色。B总数统一变成9，但红蓝绿的数量随分支不同。
答题过程
展开
The first branches, for bag A, are R , B and G .
The second branches, for bag B after the transfer, are:
| First colour | Red from B | Blue from B | Green from B |
|---|---|---|---|
| R | |||
| B | |||
| G |
Branches of probability 0 may be omitted.
(b)
解法一
思路
展开
同色路径有红红、蓝蓝、绿绿三条，绿珠虽然只有一颗，也可被移入B后再次选中。
答题过程
展开
(c)
解法一
思路
展开
分子是蓝蓝，分母须把第一颗为红、蓝、绿而第二颗为蓝的全部路径相加。
答题过程
展开
Write for blue from bag A and for blue from bag B. Then
while
Thus