题目
The probability that it will rain on any given day is . If it is raining, the probability that Aran wears a hat is 0.8 and if it is not raining, the probability that he wears a hat is 0.3. Whether it is raining or not, if Aran wears a hat, the probability that he wears a scarf is 0.4. If he does not wear a hat, the probability that he wears a scarf is 0.1. The probability that on a randomly chosen day it is not raining and Aran is not wearing a hat or a scarf is 0.36.
Find the value of .
题目中文翻译
任意一天下雨的概率为 。若下雨，Aran 戴帽子的概率为 0.8；若不下雨，他戴帽子的概率为 0.3。无论是否下雨，若 Aran 戴帽子，他戴围巾的概率为 0.4；若他不戴帽子，他戴围巾的概率为 0.1。随机选择一天，当天不下雨且 Aran 既不戴帽子也不戴围巾的概率为 0.36。
求 的值。
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
解法一
思路
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不下雨、不戴帽、不戴围巾是一条连续条件路径，分别取补概率。
答题过程
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Thus