题目
A bag contains 9 blue marbles and 3 red marbles. One marble is chosen at random from the bag. If this marble is blue, it is replaced back into the bag. If this marble is red, it is not returned to the bag. A second marble is now chosen at random from the bag.
(a) Find the probability that both the marbles chosen are red.
(b) Find the probability that the first marble chosen is blue given that the second marble chosen is red.
题目中文翻译
一个袋子中有 9 颗蓝色弹珠和 3 颗红色弹珠。从袋中随机取出一颗弹珠。如果取出的是蓝色弹珠，就将它放回袋中；如果取出的是红色弹珠，就不放回袋中。现在再从袋中随机取出第二颗弹珠。
(a) 求两次取出的弹珠均为红色的概率。
(b) 已知第二次取出的弹珠为红色，求第一次取出的弹珠为蓝色的概率。
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
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第一枚红不放回，因此第二次共有11枚，其中2红。
答题过程
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(b)
解法一
思路
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第二枚红可能来自先蓝后红或先红后红。先蓝有放回，先红则不放回。
答题过程
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Using (a),
Hence