题目
A box contains 3 red pens, 5 blue pens and 2 green pens. Lui chooses one pen at random from the box and keeps it.
A green pen is added to the box. Mira now chooses one pen at random from the box and keeps it.
(a) Find the probability that Lui and Mira both have a blue pen.
(b) Find the probability that Mira’s pen is red.
(c) Find the probability that Lui’s pen is red given that Mira’s pen is blue or green.
题目中文翻译
一个盒子里有 3 支红笔、5 支蓝笔和 2 支绿笔。Lui 从盒中随机取出一支笔并保留。
随后向盒中加入一支绿笔。Mira 再从盒中随机取出一支笔并保留。
(a) 求 Lui 和 Mira 取到的都是蓝笔的概率。
(b) 求 Mira 取到红笔的概率。
(c) 已知 Mira 取到蓝笔或绿笔，求 Lui 取到红笔的概率。
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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先取走一支蓝笔，加入的是绿笔，因此第二次抽取时仍有10支笔，但蓝笔只剩4支。
答题过程
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(b)
解法一
思路
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按Lui取到的颜色分类。每一种情况下先更新红笔数量；取走一支再加入一支，第二次的总数仍为10。
答题过程
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Write for Lui’s colour and for Mira obtaining red.
If Lui takes red, 2 red pens remain; otherwise, 3 remain. Adding a green pen restores the total number of pens to 10. Hence
(c)
解法一
思路
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条件是Mira取蓝或绿，分母可由(b)取补集。分子是Lui取红且Mira不取红，需要按取红后更新的笔数计算。
答题过程
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If Lui takes red, Mira has 8 non-red pens out of 10 to choose from. Therefore,
From (b),
Thus